IMO, they should just go all out for this Spider-Man film and take advantage of the size of Spider-Man's rogues gallery. Unlike Batman or the Flashs' villains, the majority of Spider-Man's core villains are rather stock and generic. While there are some exceptions like Norman Osborn and Doctor Octopus that have more fleshed out characterizations, most of Spidey's villains are just typical criminals/robbers.
But we can use this sheer size of Spider-Man's rogues gallery to demonstrate that we have a Spider-Man that is somewhat established and pretty much fully demonstrate that the film doesn't need to retread over the origin yet again. And without the need to focus on the characterization the villains, we can use that focus on Spider-Man and his large cast (Mary Jane Watson, Gwen Stacy, Harry Osborn, Miles Morales, Flash Thompson, J. Jonah Jameson, Felicia Hardy and Aunt May).
For the core villain of the series, I think it should be Norman Osborn played by Bryan Cranston. Rework Osborn and Oscorp to be the one who fills in the void created by the military industrial complex's loss of Tony Stark/Stark Enterprises and Justin Hammer/Hammer Industries. While having Oscorp be responsible for EVERYTHING the way they were in the Amazing Spider-Man series is stupid, I feel like they should be a major influence of the events going on. And I envision Norman Osborn to be an awesome mix of Lex Luthor meets the Joker.
And for the first film, I think the first villain should be not just one, but the Sinister Six. What better way to establish an established Spider-Man and to show just how he has dramatically changed New York City by having villains come together to plot to take down Spider-Man. And the roster of the Sinister Six should be Doctor Octopus, Sandman, Vulture, Electro, Mysterio, and Scorpion. They're hired by the Green Goblin to take on Spider-Man, but they're not Oscorp creations the way the villains were in the Amazing Spider-Man series. The Green Goblin wants to control them, but he can't. Spider-Man needs the help of Black Cat to take them all down....paves way for Black Cat spin-off film.
Second film, I think Spider-Man should get the black symbiote suit in Avengers: Infinity War to help take down Thanos. While the suit was useful in taking on Thanos, it has now made Spidey more aggressive and alienates him from his friends. He ditches the suit and Venom/Eddie Brock becomes the villain. Paves way for Flash Thompson/Venom spin-off film.
And final film a semi-two parter, ends with the showdown between Spider-Man and Norman Osborn. The results of the final battle leave Peter feeling defeated due to the death of Gwen Stacy and temporarily gives up being Spider-Man leading to a Miles Morales Spider-Man film who tries to pick up the pieces from there being no Spider-Man in New York City.