What should I expect from MM1, 2, 3, 4-5, and 6? Which ones are easier, which ones are more in-depth, does #6 show NPC's unlike 4-5?

You can basically divide the games into three sets: games 1 and 2, games 3-5, and game 6.
Games 1 and 2 are very oldschool, made in 1986 and 1988 respectively. Most info is just text, except for the very rudimentary first-person viewport. You move on a "grid", i.e. one square at a time, and can only turn in 90 degree intervals (similar to the movement in Stonekeep, if you've played that one). They are entirely turn-based, for both movement and combat. These two are often considered to be quite hard. The design for these involves very few formal quests, and a lot more wandering and exploring, with the ability to go pretty much anywhere you want right from the beginning. Pretty much all items in the game are found as random loot from fights with monsters, so there aren't any points where solving a specific dungeon will reward you with a nice weapon or anything like that. Items also don't have any info on their stats, but the cluebooks that come with the games give item stats. Combat occurs on a separate screen, showing a list of enemies and giving you options for each character. Like the rest of the games in the series, it's best to use a well-balanced party with both fighters and spellcasters, and it's almost essential to have a robber. These games have some limits to their depth based on their age, but in terms of stats and items offer a decent amount, with MM2 of course adding more items and allowing the player to raise stats to higher levels. In the first game the player will have to make his own maps on paper. In the second game there is a rudimentary automapping feature, but there are still many reasons to make one's own paper maps. Automapping is improved in the later games, making paper maps unnecessary.
Games 3-5 still use the grid-based movement, but now you can see enemies in this view, and there is no separate combat screen. The game is still entirely turn-based. Ranged combat with bows and spells now exists as a way to harm enemies from afar, whereas in the first two it was simply a different mechanic in the combat interface. I actually haven't played 3, but I've played 4 and 5, and they have a lot more formal quests although the game still involves heavy exploration. Many consider 4-5 to be the best introduction to the series. They are also easier than the first two games, while having more depth to the world and more items and equipment, including different materials for weapons. At many points specific items and equipment are found as quest rewards or in specific locations like treasure rooms in dungeons, so loot is not entirely random like the first two games. Games 4-5 merge into a single, huge game with many hours of gameplay, probably the most in the series. In terms of traditional RPG systems, I would say these games probably have the most depth of the series. In 4-5 at least (not sure about 3), you can save your game anywhere, unlike the first two games where you could only save at an Inn, so that's a nice feature. Games 4-5 also feature a lot of puzzles, such as passwords to work out, traps to maneuver through, etc., and many of the dungeons are very involved in this regard, which helps give each location a unique feel. The biggest drawback of these games in my opinion is that items stats are still not provided, and with the addition of different materials for weapons make it really hard to determine what you should be using. Fortunately, the cluebooks that come with the games still provide all the item stats.
It should be noted that for all of games 1-5, a lot of the world exploration is technically optional. I found that if I took time to explore everywhere, I did not have much need for grinding (I only really did grinding in MM2 because I was trying to finish some optional challenges that are much harder than the main plot endgame). Those who want to follow the story and not explore around may feel the need for some grinding though.
Game 6 has the most changes from the previous ones. It is fully 3D from a 1st person view, and the player can move the party about freely. It does show NPCs walking around the cities, rather than just in select locations like shops in the earlier games. The game is in real-time but at any point can be "paused" and moved into turn-based mode. I used turn-based mode for the majority of combat, although easier fights can be done in real-time. Characters now have full "paper-doll" inventories with graphical representations of items, and dungeons and other locations are fully 3D and therefore take advantage of the third dimension with stairs, ramps, pits, etc. The game has a LOT of combat, and is generally considered to be pretty hard just due to the sheer masses of enemies you need to fight through. Outdoor areas especially suffer from huge mobs of enemies. The game is technically open in terms of where you can go but the difficulty of enemies makes most players follow a certain path through the world. The amount of quests and such is equal to if not larger than games 4-5, with most dungeon visits being motivated by quests rather than simply exploring. General exploration is definitely still rewarded though. In terms of RPG depth, some aspects are deeper than the previous games and some are shallower. You only have four characters instead of six, but they now have a set of skills pertaining to weapons and armor that allow them to specialize in certain types (i.e. daggers, swords, staves, bows, etc.). The magic system is revamped with some that are really useful, but if one doesn't know where to find specific spells it can make certain parts of the game much harder until those spells are located. Loot is mostly randomized but there are many specific treasure locations that always contain loot of a similar quality (for instance, a specific treasure chest at the bottom of a dungeon will always have something good, even if it isn't always the SAME thing). It seemed like there was less variety in loot and magic spells, but that most of the spells and loot were useful. I thought that 6 did a decent job keeping the "feel" of the series but that combat got a bit tiresome, and the endgame got a little boring. Also there are many times when you need to locate NPC trainers to raise your skills, and end up having to try entering basically every house in a city before you are able to locate them. Finding specific NPCs was probably the second most tedious part of the game after the combat.
My personal favorites in the series are 4-5, although again I haven't played 3 yet. I will say that starting from the beginning of the series allows you to see some overarching plot elements and concepts that continue through the series, which is pretty cool, but overall the games are quite separate from one another, taking place in different worlds. Starting with the first game can be a bit rough since it's so old, even MM2 has noticeable technical improvements. Game 6 also has a plot that intertwines with that of the Heroes of Might and Magic series, which is pretty cool.
I hope that helps!

Why, thank you, Waltorious, for this extensive answer! I have another question for you.
I have read somewhere that characters could age and wither in the M&M series. Since I prefer taking my time when playing an RPG, the idea of being "too slow" has prevented myself from beginning any installment in the series. So, could you tell me how is ageing taken into account?

Unless you are doing something very unusual, there is definitely a lot of time.
In MM1 and MM2, each level is a year. Every time you gain a level, the character gets one year older. Shouldn't be a problem.
In MM3, 4, and 5, time passes regularly as you walk; each step counts as a certain amount of time depending on the terrain and certain other factors. As you get older (up around 60 years or so) you start to lose some stats. Most importantly is your endurance, which will kill you beyond resurrection if it reaches 0.
I can complete World Of Xeen (MM4 and 5 and the special bonus dungeons you only get when they are combined) going through all dungeons, including the optional ones, getting 100% kills and almost 100% steps in about 10 years of game time. An amateur should have no problem doing the same in 40 years.
The only way you can really lose time is by "working". It's possible to go to Rivercity and work for a week. This is a good way to make money (especially if you're putting the money in the bank for interest) but you can quickly work away several years of your life doing so without noticing.
Also, getting lost in the desert will waste a lot of time. If you go into the desert without the Navigator skill you'll lose a day ever 2 steps. It can take years to get across the desert that way.
No idea how getting old affects MM6.

Thank you, Stan! Now I don't have any reason to postpone this journey!

In MM6 time passes at its own pace. So just standing around for some time, the night will come, etc. Also training for the next level takes certain amount of time (not sure about how big it is) and travelling between locations takes certain amounts of time. 2-5 days, IIRC.

WizardStan is right, I just wanted to add that in MM1 and MM2, you can reverse aging, even natural aging. There's a spell called rejuvenation that will make your characters younger (or older if it fails, but usually you can get it to work), no matter whether they were naturally or unnaturally aged. So you definitely don't need to worry about it there. And, as he pointed out, there's no problem in Xeen either as there's plenty of time to do everything (watch out for unnatural aging in Xeen, though... but that can be reversed).
Also, klaymen is right about MM6, there's a standard time cycle going, and certain actions like traveling will take several days. Training takes one week, if I remember correctly, but I never had a problem with my characters getting too old. Mainly it's good to know that training takes a week because there are certain things that need to be done on certain days of the year. It sucks to miss that because you thought you had time to train first!

Oh yeah! Good catch on the unnatural aging. I'd completely forgotten about that. It's possible for characters to get so old due to that they do start dying of "natural" causes, until you undo the unnatural aging, as you say.
There is also one other saving grace: if your characters do get too old, just create some new ones, go to the Warzone to gain experience, and use the huge amounts of money that your former characters had no doubt collected to level up quickly.

on the darkside it gets really easy to undo the magical aging, so that shouldn't be an issue if you plan it right.

On certain versions of the game (by no means all of them) extreme age does negatively impact your stats. But you will most likely only have this happen magically; ninety years is a tremendous amount of game time in Might and Magic VI. It's also a LOT of magical aging, and I've only had it happen from using a certain spell; it is also easily corrected. I think they removed the ability to die from natural causes, due to the fact that your party is now a fixed group of characters and therefore too much magical aging would end the game for you.

IIRC, In MM3-5, a week is ten days long, and a year is ten weeks long. So if you work for 90 weeks to earn enough interest at the bank to be able to afford to train for ten weeks (this is the sort of thing you find yourself doing in MM5 because money is so hard to come by), you can find that ten years have suddenly flown by.