There will be totally separate character storylines for each character (this doesn't mean that other girls can't appear in said stories). As for the main storyline, that will just be for unlocking new content as I have it ready and perhaps some additional challenges. The main focus of the game will be in the school, club, girls' storylines and random/world events.
But as it's still v0.051, it's a super early version, so there's not super much content yet. If you want to see an example of a character's storyline, try raising Natalie's affection and talk to her in the library.