I actually put far too much thought into this type of thing. In most cases, my character is a make-up of different supplementing and complimenting attributes from me. If anyone has read up on Carl Jung's work, you could compare my character to the Anima.
Generally, the supplementing attributes would be things like how our thought process works (in an analytically way, in most cases), or how our tastes stay roughly the same. She likes video-games, I like video-games. She likes pizza, I like pizza. She's kind of lazy, I'm kind of lazy. And we both believe in the same sort of thing as well as having roughly the same intentions from our actions.
Though for the complimenting attributes, it comes down to opposites. The largest one is that she tends to be much more aggressive, assertive, brash and blunt about things, whereas I'm more submissive, timid, cautious, and mindful. Even with the same kind of mind set, she approaches things a bit differently due to this. Her personality also tends to work better within a game where you're, you know, killing things. The other large one is she's female and I'm male, but that's solely due to the suppressed gender opposition then anything else. Oh, also, she likes the color purple, whereas I've always liked yellow; about as complimentary as it gets.
It's not a gameplay related thing (we both generally like to play the same sort of games), it just works well to project her onto the avatar then myself, since she's not really me, and the avatar in the game isn't really me either.
This isn't needed, but I drew it recently so I might as well post it; some doodles of her:
Generally I play a melee character that fits her. Maybe with some magic as well (like lightning, I like lightning :P), but being able to smash faces is still primary.