I wanted to play a Clint Eastwood like gunman character, but my gun keeps exploding in my hand or something and killing me. What am I doing wrong?

A gunfigher is a lot harder to play as than a magic/melee character. Stick points into perception and firearms and in Shrouded Hills do the quest for the Doc and he will give you a decent starter gun. You also need to pay more attention to target info too, line of sight...stuff like that.

You need to have some points in Perception and Firearms for more success (and less critical failures).
Also remember that Technology and Magic do _not_ get along. Having magical armor and wielding tech weapons can lead to some really surprising results. The more tech 'attuned' you are, the less chance that catastrophic things will happen - though that also means that magic items will work less for you (or not at all).
I am not sure how having virgil as a follower tips the balance (if it does) - Virgil is a magic user, and by the laws of Arcanum his very presence can cause tech to act oddly.

i think if your a tech char, Virgils healing spells just get more and more useless

Indeed, Virgil's spells very rarely work on you if you have a high enough tech rating. The few times they DO work are often critical moments (at least in my experience) where I really needed that major heal or resurrection, but don't rely on that.
Other than that, there's no effect on either of you if you're a tech character with Virgil (or any other magic character) in the party. Would have been an interesting twist, though; forced to either suffer their magic interfering with your technology, or to keep only technologists and middle roaders in the party.

And don't forget take a lesson in Firearms to obtain a degree of Student(?). It can help reduce the critical failure. Or maybe expert or master.

Default Arcanum seems to favor magick-users greatly over tech-gunfighters. Search for "Krupp's Ranged Mod" on the Terra-Arcanum website for a user-created patch that seems to bring firearms more in line with swords and spells.
Also, the firearms mod does seem to work fine with the UAP mod.

I'm having a blast (pun intended) with Molotov cocktails! Rags can be found in the trash cans and fuel is relatively cheap, costs about 11coin per cocktail. Even with no throwing skill points, it still does some great aoe damage and knocks the enemy away several paces. It also doesn't do an friendly damage. Bombs away!

My first character was a gun fighter. The problem I have is that bullets cost so much that I can't afford to use it. Also since I'm full tech, Vigil can't even heal me. I've since given up on that character.

It might be worth keeping Virgil story-wise, but as a tech char he is kinda useless.

It helps when you buy the schematic for bullets, then it's just a matter of finding or buying saltpeter and charcoal.

1) there is a healing npc for tech char.
2) You can make your own bullets.

I'm gonna check that out, thanks!

Bullets have not been concern as stealing is extremely lucrative. Instead what I have been finding is that the limiting factor to how long I can explore/dungeon crawl is the amount of healing drugs the tech healer can carry. Personally I am finding the tech healer a little lacking and don't have the patience to really search for herbs.
Also, I'm not sure if the game is going into hyperspeed as many older games are prone to on newer systems. What I do know is that as a level 21 gunman I took on a lvl 35 elemental multiple times in both turn-based and realtime combat. I found that real-time effectively constitutes an IAS for constantly attacking ranged characters compared to turn-based. Enemies that were impossible to defeat in turn-based mode easily fell to my basic repeating rifle. That said I'm going to be trying more called shots in turn-based and see if that can make up the difference.

Very quick startup guide to playing tech based chars:
Take one point of persuasion. You need it to get out of the shrouded hills. Your aim is to get to Tarant asap.
Do the absolute minimum of ighting: you can handle, with Virgil, all the lvl1 monsters and a few of the tough ones, but it's very hard work. Avoid combat until you're ready.
Get to the shrouded hills, and do the easy quests (the Doc Roberts fight should be doable and gets you a decent pistol). With that pistol and Virgil you should survive the trip to Dernholm.
Take the Dernholm quests. Get up to Black Root, finish the taxman quest and return. Make sure you keep 150 gold for the train fare to Tarant out of what you earn/collect.
Get to Tarant. Again, do the non-combat quests.
At this point you should have hit level 5+. You need to have spent your points on at least one of the following ways to kill:
3 points in firearms/melee + expert training
(1pt + apprentice is good enough if you supplement with other combat skills)
1 point in (make molotov cocktails) + 1 pt in throwing (+ apprentice)
(this is almost essential for crowd control)
1 point in mechanicals to let you build traps
(running the tough monsters over spike traps can be very handy)
3 pts in persuasion with expert training
(Let your followers do the killing for you - note you get mucj less combat experience this route)
Using these in combination with making/buying equipment makes you as capable as the starting mage. Obviously not as straightforward, but you should be able to head back from Tarant and complete all Mine, Wolf Lair, and other dungeons fairly smootly.