Spiderman - let the guy be an actual teenager, that's what the series was all about, a 15 years old geek who gets these amazing powers. Oh, and the most importent thing, Spiderman must never and I mean NEVER stop talking while fighting.
Gwen stacy - Actully introduce her from the start, have her as Peter's first love interest, until her expected death.
Mary jane - Do a proper Mary jane this time, not that whiny thing that Kristin dunst has played in the films, but the ultimate redhead who is everything Gwen stacy is not.
Marvel universe - I can't start to think how cool can it be to have Spiderman always comparing himself to the major super heroes in the business, such as the avangers.
Villains - Lizard should make a great bad guy if done right, followed by the goby and Doc Oc, and later on... Venom! (And I mean the real venom and not that alian rip-off in Spiderman 3, a guy who actully torments both Peter parker and Spiderman throught the entire film)