I haven't played it, but Axis practically explained things for me. I'm a sucker for girls who have had horrible pasts but then act like thaaaat D: I didn't know she was psychotic till later, but after I learned that, it was too late.
Well, I admit I don't know the story well for GG, but I don't know, none of them appealed to me greatly. (Except Slayer) I bet if I did get into the story more, I'd be able to pick a character then. But I barely have access to the game as it is, so yeah.
Real talk, when I first got BlazBlue, I was stuck between maining Jin or Bang. But then I played story mode and LOVED Ragna's story (And Bang's story made me lol), so I ended up choosing them to play as. My tastes are probably ridiculously specific xD
(Also, in Naruto fighting games, I always picked Gai. For the same reasons I pick Bang)