I still can't believe they are going to reboot the Spider-Man movie franchise. And why on earth would they go with Ultimate? Well, since this IS happening, here are three things to keep it from becoming a rehash of the first film, and to make a decent movie.
1. Skip the origin. Spider-Man's origin is the most well-known origin in comic book history. (Maybe even more than Superman's) Instead, go with the way the 90's Spider-Man or Spectacular Spider-Man show went. Just start the movie out with a bunch of robbers, and he webs them up.
2. Keep away from high school drama. Since this film is taking place in high school, the "drama" should be kept at low scale.
3. Don't make Peter immature. In the Ultimate universe, Peter Parker is not exactly as mature as his 60's counterpart. Keep him nice, smart, and caring.
And those are three things that I think shouldn't happen in the film.