[ok this is like almost 2 years old, but I just re-discovered it in my documents, and I thought I'd post it.]

In a story driven game, it’s always a good idea to have the player look at the main character almost as a mirror. There are three ways to approach this as I know of (please respond if you know more):

1. Give the player a character, with core values (usually the standard virtues) and let him/her 'tweak' it to match their attitudes. This is the most common road taken. FF7 does this, FF8, Legend of Legia, god the list goes on and on. Sometimes, they can go as far as to make alternate endings for each due attitude.

2. Create-o-matic character generator! I'm not really big into these, as my bias will tell. Here you actually get to make a character however way you want! Even yourself, what could be more immersive than that? The problem is that no matter how much time you spend on the limited details you can adjust, the end result will always be a body builder in skin-tight clothes. "Yeah that's totally me". If you decide to make the character at least half representational of yourself, or if the game just doesn’t give you the option (ie freeware MMO’s) to make your character a god, the result is even worse. The create-o-matic then spits out a starved crack whore that has escaped from the circus. It’s really one end of the pole or the other. When you get bored of the game, you find yourself trying to make the sickest character that only a mother could love… if she was drunk. Wait, I haven't started on the story yet! Now you have to guide your little crack whore through the game. In the end you say "Wow, I (the character who symbolizes you) had some unique adventures, and I saved the day in my own way!" You enjoyed the experience so much that you tell your friend to come over, so he could try it too. It’s all smiles until you notice he is the same cool super-buff model you chose. What are the odds?! As the story progresses you realize it's the same cookie-cutter dialogue that you called unique. Does anyone remember playing The Sims (1), and how EVERYONE picked the same the guy with the shades and bleached spiked hair?
This reined is the supreme approach to character immersement
On paper, this looks like the best idea on Earth, but in practice it just falls to pieces.

3. Another biased argument figuring that this is the approach I am probably taking in my fighter.
You choose the character that suits you best from a selection of (hopefully) different characters. One of the only draw backs of this approach is that it often re-enforces stereotypes. The character will embody what the world thinks a person of his/her type consists of.
Anyways, here a player looks the character over, and reads their bio. If something resonates with the player this will become his avatar. This is what I feel selection should be based on. Most of the time though, it depends more on finding the character that isn't exactly balanced and gives the player an edge. Even if the back-story for the character makes her a crack whore circus runaway.
Just to point of the obvious, here are some advantages to using the method over the others:
1. A player can have a unique experience as opposed to his friends.
2. Can learn a lesson, or answer a question that they could be dealing with.

I like games that are epic and give a character to you, BUT doesn't say anything, but you know he or she is really bad ass. IE Half Lifes Gordan Freeman (on a sidenote I just beat half life 2 and half life 2 episode 1 and I'm now working on episode 2) Legend of Zelda's Link, and some other games I forgot.