Been experimenting with different party builds, and I'm curious to see what yours have been. I just did a party full of cat ninja, all with the same face and voice, and it was hilarious. No one could hit them, but they weren't that effective either (as could have been guessed).

Almost anything can be made to work if you're sufficiently familiar with the game. Are you interested in oddball parties for experienced players or more so in failsafe parties for new players? The answers would be very, very different.

Good question! "Oddball but Effective"

Like, it's surprisingly fun to play a single lone ninja, for example.

It's also a lot of fun to play with a completely mundane party. Fighter, Rogue, Gadgeteer, Bard, and maybe RFS-81. I'd recommend using the Cosmic Forge editor to change Identify scrolls to cast at level 6 instead of level 4, though, or you might have trouble identifying some of the better bard instruments.

Lord/Samurai/Ninja is a pretty fun group too. You won't have Haste, but you shouldn't really need it.

Really, as long as you have a decent spread of magic schools and armor types, you should be fine with almost anything. The only classes I've ever actually soloed all the way through have been Lord and Ninja, though.

There are the "rules" that I created for a very good party

I found that the best way for me fight in the endgame is to have weapons with reach.
Reason: This allows me to fight all the annoying long reach creatures without having to move every turn (forfeiting initiative). If you need a quick spell to heal up your dying party member moving isn't the best option as it will typically let everybody else go before you and unload their dps on your party before you will be able to act.
Also, staying at reach will prevent those long-limbed critters eating your casters alive. If you move to short range they can reach them.

Always max stats. Choose two that you will exclusively race to and then do whatever you like.

With a front line figher I ALWAYS go for strength.
Why? Because then you'll hit like a truck, you'll penetrate every armor (almost always hit), your party load will be higher and you won't use as much stamina compared to speed builds. All these reasons are very important for me. I simply hate when I see that I am tickling the enemy with a non-100-strength character and my 100-strength character mangles an enemy per round. Such a character is hardly justifiable. But then, those occasional stuns and deaths are not bad, but it's just... ...random. In my experience a warrior can typically kill at least one enemy (Rapax Rift comes to mind now) with pure damage while if a class relying on other means doesn't get lucky you might be left with an enemy with 80% health left easily.
Why is load important? I don't like returning to town unless it's absolutely necessary. That means that when I buy consumables (Arrows, stones, sniffing salts(?)...) I buy them in bulk. Add to that that your front liners wear some heavy-duty armor that is not exactly light and you gather things as you go. This can easily become a major nuisance if left unchecked. I was constantly getting into blue load sometimes even more with non-strength characters. Moreover strength increases stamina which is very important. You can last longer in combat, you tire slowly and thus you are longer effective.
Having and not having stamina may often mean in prolonged fights that your party member falls unconscious and enemies will almost certainly kill him. In my first party I have had a very harsh lesson about making speed builds with my engineer. With his fully upgraded rifle he drained ALL his stamina during one round. ...seriously. He WAS freaking deadly, but then he was also very often dead too.
Also strength governs bow, sling and thrown weapons damage too (if I remember corrrectly).

My second choice for melee characters is Dexterity.
There are other interesting options too, especially vitality imo. i prefer Dexterity because it gives me more defense. Vitality let's you soak more damage. That means moar mana drain on healer. Iron skin IS nice, but that's all it does. More damage soak, better stamina and I thing slightly better load. The thing is that I don't need that extra hp in endgame. Dexterity at 100 gives you nice damage mitigation on itself PLUS more attack (so more damage) and I think it improves hit mechanics (To Hit?).
Going for vitality with warrior will create interesting situations. Hell, it even saved me a lot of times when I had that build. You may actually destroy all the enemies 10 rounds after the rest of the party died but the ressurection powders are so expensive... ;) And I sell most of them anyway.
That being said vitality IS a good stat. I just prefer Dexterity.

Vitality:
Good to raise after you have reached your two primary stats goal. Where at melee characters you struggle to choose the the "right" stat, Vitality is a huge deal for casters. Seriously. Go for your main stat and vitality. Game will be a breeze. There is a serious difference between a 100hp mage and 200. You might even cast a few spells in the endgame before you die. I ALWAYS go for vitality + piety with my healer. He has to stay on his feet and those two stats (along with damage reductions at 100) do exactly that.

Piety:
I take it as a main sat for priest ofc and I try to get some with other casters after I have reaached my first two 100-points-stats. Iron will is fabulous.

Intelligence:
Now intelligence is to offensive casters to what is strength to fighters. And I can't stress this enough: If you don't have Power casting in the endgame you are ROYALLY SCREWED. Your mage/psionic/whoever will be reduced to support role and try to get some cc on enemy because his damage spells burn enemy Rapaxe's eyelashes and itch him to annoyance at best. I have made this mistake once and I will never do it again. Almost every monster later on have 100+ resistance to spells (With the "weak" ones at 80). Must be.
Intelligence is a very nice choice for 2nd set of maxed stats for non-offensive casters.

Speed:
While nice stat in my experience it's not a good choice. You have more important stats to choose from and this is a 2nd-round choice. Snake speed is rubbish imo (expecially when you need to move in the round). Melee characters with too much speed tire so quickly (you probably don't have enough stamina since you have chosen speed over a stamina-abundant stat), casting that fireball before the enemy is not that vital in the long run. There are moments when it comes handy, even might win you the day but would I choose it over Intelligence, Strength, Dexterity or Vitaliy? No. 2nd choice? Perhaps.
The only moment when it comes handy is a quick heal before enemies can act but then my priest doesn't exactly prioritize speed.

Senses:
Wasted stat. Except for ranger. You CAN choose one character for it for searching purposes but I wouldn't build a strategy around it. Now if you wanted a ranged party, that would be an entirely different story...


Races:
I don't have any strong preferences except I take dwarf as my priest and I choose something with high starting strength for my warrior (Lizard). This is because once I have my maxed warrior the rest of the party can slack. Really. They are THAT good.


Classes:

I always have a priest.
I always have another caster for buffs (usually a mage).
I almost always have a warrior when testing new stuff as whatever I screw up I know that all I need is that warrior and enough time. Warrior is the most overpowered beast in the game in my experience. It's an unstoppable killing machine. Especially in the beginning... Monk: Bam 6 hit, swoosh 3 hit, Valkyrie: -thrust- 13!! hit, Warrior: 40-freaking-kaboom-heads-and-limbs-flying-around-next-please!!! This doesn't stop even in late game. Hits over 100 are a norm for him.
Keep in mind that your hybrid won't do much damage with spells in endgame if he doesn't have Power casting. In this having a samurai with intelligence 100 (And Power casting) makes a lot of sense if you plan to hurl fireballs at Rapax.
I try to have 3 characters that can stand in melee.
Rest is up to what i feel.

Conclusion:
1st spot: Warrior. Go for Strength and Dexterity.
2nd spot: Priest. Piety, Vitality.
3rd spot: Mage. Intelligence, Vitality.
4th spot: Melee with reach and possibly utility. Valkyrie with halberd is a very nice choice. Offheals, can survive death, has bonus on halberd and wears heavy armor. You can go Strength Dexterity with her. She's not an offensive caster by nature (although you can get nice priest spells later on too).
5th spot: You might want 3rd melee with reach that fills in the magic school you lack. Monk can be a very nice choice. But don't worry to experiment.
6th spot: Ranged or caster. Again, based on what you lack. I tend to use ninja here as they can open locks (although i suspect it's redundant with casters and strong warrior), cast spells and have critical on thrown weapons. Just make sure not to waste too many points as you can get jack-of-all-trades who can't do anything properly.


I ask the readers to take into consideration that this post was written based on my experiences and represents my opinions on the game. If you have a different one and disagree with me, do so in a polite and constructive manner, please. Explaining your opinion is a great first step towards a dialogue. :)

Fantastic stuff! Thanks for taking the time to write that out =)

My take is a little different and of course mostly rooted in my personal preferences (such as my hatred of 'furries' and thus refusal to include Rawulf or kittens).

Slot 1: My tank which is usually a Dracon Samurai because of breath weapon (can help in early game or clearing out hordes of small critters), speed and critical hits.

Slot 2: Usually I have Vi Domina (human Valkyrie recruitable in Arnika)) after I get to Arnika and rescue her. Her extended halberd reach remains useful for killing distant enemies (IMO even more so than sticking her in a back row) and she makes a decent back-up healer/buffer . There are options to replace her with the Android Monk (RFS-81) or a T'rang Samurai or several other RPCs later but I seldom do so. Sometimes I replace with my Fairy (converted from Mage to Ninja and using Cane of Corpus).

Slot 3: Miles (human thief recruited in Arnika) just because you get him early and by the time you find a better replacement you will have invested a lot into developing him. Sometimes I replace with my Fairy (whom I convert from Mage to Ninja), taking advantage of ranged criticals.

Slot 4: Mook Gadgeteer - The race does not really matter too much as a dwarf or gnome can do just as well but IIRC it helps at some point to have a mook in the party. Gadgeteer because of the Omnigun and the many useful gadgets you can construct in game. Can recruit a Trinnie Gadgeteer in Trynton if you do not create one.

Slot 5: Female Elf Bard - Must be female elf because of useful item to be found later. Bard because free sleep spells and the TON of very cool, very useful instruments you will find. If you do not create a bard then you can recruit an Umpani Bard in the Umpani city/base.

Slot 6: Either an Alchemist or a Bishop of either Elf, Gnome or Fairy race. Alchemists make random potions while camping which can be used or sold for money.

Slot 7: Gnome or Dwarf Priest for Divine magic/healing.

Slot 8: Fairy Mage (will later change to Ninja).


I do not bother with Rangers because, while their detection/scouting ability is nice, it is hardly a necessity and they are at best mediocre back-up healers and as far as ranged fighting goes gadgeteers far outclass them.

There is nothing wrong with Lords as far as stats and abilities go but I just have a personal issue with the gender specific class name (why not call them "Paladins" or "Crusaders" or some such?!) so I don't use them.

Monks I do not tend to use because I personally would rather have a well armed and armored tank dual-wielding a couple great swords than to have the unarmed Shao Lin knock-off.. On rare occasions I will recruit RFS-81 (the android) though.

As mentioned I avoid 'furries' so the Puppy and Kitten races are unused by me.

Other than that I pretty much stick to the tips others have provided here.

My parties are usually more magic heavy, because I prefer dealing more damage overall and the versatility. I think this makes the beginning of the game easier. In later stages of the game, you need to take care of enemies one at a time, but you can do that with just one or two fighters/hybrids with Guardian Angel and Body of Stone. I'm also biased towards weapons with long reach for reasons already mentioned, so usually everyone have staves or spears.

Example:

Dwarven Fighter - A tank.
Ninja - mainly a thrower and a lockpicker. The autopenetration is especially useful in the beginning. It's also nice to have someone to be able to use the powders and potions early on. Put him in the front line in order to increase the stealth ability. I also like to increase DEX and SNS first, then STR so that most of the skills increase faster and Reflexion is unlocked faster. STR isn't as good for ranged as it is for melee anyway.
Alchemist - Good for dealing damage and also good for defense. I'd increase mainly Alchemy and Mythology on level up.
Bishop - A fast bishop for getting protections up early in combat.
Mage - My favorite for dealing damage. Usually first in combat if Fairy.
Bishop - A slow bishop with more SP.

I've tried this setup until Arnika on Ironman Expert difficulty, and they've been very effective. The only issue is the start of the game where the mage has 5 hit points or so. I avoided the noxious slimes until level 2 and avoided Gregor until level 4. Always be cautious against higher level enemies no matter what party you use. For later parts of the game, adding a NPC like RFS-81 would speed up combat somewhat, especially with Zatoichi bo.

Some stats can be more relevant to a character than they initially seem.

Senses is one example. It's not an obvious choice for a fighter, but the initiative boost still applies, the skill (and Eagle Eye) can be useful for him if an enemy is at range (since he doesn't have casting options and won't hit the broad side of a barn later on without it), and more subtly, it's the first governing stat for Close Combat - his primary skill. A Fighter with low Senses and Intelligence (like the default lizardman) is liable to see that skill stagnate after a while, which really hurts his long-term development.

The good thing about Wizardry 8 is that any party is possible. My current game consists of what I call "the Malus party", because almost all start with negative stats: Dwarven Monk, Mook Lord, Dwarven Samurai, Dracon Bishop, Lizardman Bard; the only one who doesn't have a malus at start is my Ranger because I didn't want him to be a Lizardman (too dangerous if turncoated due to ranged criticals, and Lizards get turncoated very easely), too.

Having such a party might seem like a very bad idea, but it's actually not, the main drawback is that it will take longer to get the expert skills. On the other hand they come with skills which can be quite handy for their selected classes:

Dwarven Damage Resistance and the Monks natural resistance stack, giving them very high damage absorbtion, especially if they also get iron skin.
A Mook Lord is a very rounded character with at least 50 points in every area, giving you plenty of options how to develop him. Plus the Mooks high magic resistances. Plus, he could use the Giant Sword.
Dwarven Samurai: dwarven Damage Resistance helps against his relative squishiness for a frontline combattant. Plus, high Piety means both more stamina (he'll need it in prolonged fights) and more spell points if you want to create a true hybrid.
Dracon Bishop: High Vitality means he'll survive fights much easier then his more squishy counterparts and can wield a close combat weapon much more effectively if out of magic. And Dracon Breath is a very good back-up to that, too.
Lizardman Bard: Much stamina for his Instruments and can put up more than a fight when the ennemies come close. Also, the Bard's special equipement eliminates his magic resistance deficits.

You might also notice that every hybrid uses a different spellbook in this party (Monk = Psionics, Samurai = Wizardry, Lord = Divinity and Ranger = Alchemy), meaning I have a backup for every spell.

What equipment helps him against mind magic?

Oberon's Greaves (purchasable at Antone's) give a +5 to both Mental and Divine Magic. I agree that ain't enough, but combined with the Amulet of static you find on the Arnika road on the way from the Monastery to Arnika is enough to nullify it's malus. I generally also equip him with a Philosopher's Shield later on, which gives him an additional +20 to both mental and divine

I have played through wizardry 6 and 7 both, and am just starting 8 right now. The classic awesome party build that me and my dad always use in this game are 2 samurai, 1 ninja, 1 valkerie, 2 bishops. Trust me you will tear things apart, and the endgame weapons will split up nicely, and any reflex or critical strike perm buffs give to your ninja.

My prefered party is: Fighter, Rogue, Bard, Gadgeteer, Priest and Mage.

Priest and Mage in order to get all buffs.
I am too lazy to use more than 2 magic users (=adding an Alchemist and/or a Psionic), since casting spells is more micromanagement than hacking and slaying.

Gadgeteers are strong in the lategame and have access to "heal all", which is powerful.

Bards have "heal all" too and having music "spells", they can use cursed swords very well without being crippeled by not being able to use a bow.

Rogue and Fighter do massive damage and level quickly. Hybrids are more micromanagement during combat and don't do that much damage.

One could easily change the Gadgeteer to Ranger. That would add some alchemy magic.
The Bard could be replaced by a Psionic or Monk (to get the almighty "haste") but since the Gadgeteer has some Psionic "spells" as well, it might be better to replace Bard AND Gadgeteer together.