Classes in games are helpful to defined who you are and what your role is. What you lose in flexibility you gain in defined roles. Everybody had a different way of picking their characters. Here are how I picked some of my favorites, and how I picked them.
Diablo II
Class: Barbarian
this is probably the game I played the most with my friends. Why did I pick the Barb? The demo for Diablo II had only one class, the barb. I reeealy wanted to wield a crystal sword, but the demo wouldn't let you get far enough to actually be able to afford the thing. So when my buddies and I started playing I decided to revive this dream.
Borderlands
Class: Siren
When picking FPS guns I tend to go for SMGs. So I chose the Siren to complement my Shoot till I must reload strategy. I played this game with two friends. Ironically I ended up playing most of the game on my own.
Borderlands 2
Class: Siren
This time around I actually started with Zero, but I didn't like his play style. So I had my buddy hack the game to make me Maya. We haven't finished this game, since we only play two player.
Diablo 3
Class: Wizard, Male
I found out the Wizard shot lasers. Good enough for me.
So how do I pick Class based characters? Mostly it comes down to play style. I don't care about gender, though if given the option I'll play male. I don't like temporary buffs very much but I do like static buffs. If a character specializes in my preferred FPS weapons ill pick them. My preferred weapons being dual pistols and SMGs.