This just an idea that I thought would be very cool:
You would choose a character and start playing as them when their powers first surface. So if you chose
you would start where the bully is attacking your girlfriend and then you would go through his life such when he goes to Professor X's school and when he became a Defender and you would learn different powers as he learns them.
There would be many X-Men to choose from and each would have a different storyline.