When I'm playing a video game, I don't need the characters to be or look exactly like me. I'd rather immerse myself in their world and have fun with my choices and gameplay. If I have choices, I want them to have an impact on the storyline.
I prefer characters that behave and look realistic. I prefer the body shape to look realistic rather than over-exaggerated for males and females. But not realistic like some feminists portray characters so they look more like them or chubby. 
I don't want to play a video game as myself, I just want the characters to be believable.