I, personally, feel the best way to introduce the new J. Jonah Jameson (whoever will play him) would be to have it where Betty Brant tells Peter that Jameson is a hard man to approach and if he gets some pictures of Spider-Man, he'll get a chance to have a meeting with him, and possibly get hired.
During the credits, Peter presents the photos to Jameson and he could be like how Simmons played it:
"Good... good... crap, crap, CRAP, very crappy, yeesh I'm not even going to touch that. Wait... what's this? Amazing! Spectacular! Astounding! What's your name? Ah, it's not important, you're hired. Now, get out of my office in the next 5 seconds and get me more pictures or kiss this job goodbye."
It'd be nice to get Needs or Ben Urich, or Robbie Robertson in the movie.