Introduce the whol high school crowd in the first one - Harry, Gwen, Flash, Randy, Liz, Sally, Kenny, etc.. At the end of the movie introduce Gwen like how she was introduced in SSM - May invites her over to be Peter's date, he opens the door, we get the "face it tiger" line. Also introduce the Daily Bugle crew - JJJ, Betty Brant, Ned Leeds, Robbie Robertson, etc.. Maybe Eddie Brock. Ideally I'd open the movie with Spidey stopping de-powered versions of Flint Marko and Alex O'Hirn. Obviously introduce Oscorp too - Norman as head, Octavius working woth him.
In the second movie introduce Felicia as Black Cat, but never have Peter meet her outside of costume. I'd also start the movie with an action sequence of Spidey stopping Vulture.
Most of the school characters won't need huge screentime, but they'll still be present. Just having names from the comics instead of a load of random students would be good.