It Might Be A Trilogy: The plan at one point was for the Marvel/Sony deal to cover a whole trilogy of new Spider-Man movies. There was no mention of this in the press release, but if this is still the plan, Spidey may end up sticking around in the Marvel Cinematic Universe until gone 2020. It was also mentioned at the time that Marvel wanted Spider-Man in Captain America: Civil War.
Sam Raimi Could (But Probably Won't) Return: Amy Pascal at one point spoke to Sam Raimi about returning to direct or produce the next Spider-Man movie, but later didn't seem to have very many flattering things to say about the helmer of the original trilogy, so this one seems unlikely.
Joe And Anthony Russo Might Produce: After the talks between Marvel and Sony fell apart, Joe Russo got in touch with Amy Pascal to offer the services of him and his brother's newly-formed production company, Bullitt. However, they said that a "difficult conversation" would have to take place with current Spider-Man producers Matt Tolmach and Avi Arad, and it clearly has based on their demotion. Whether the Russos will produce the next Spider-Man after introducing him in Captain America: Civil War remains to be seen.
Spider-Man Might Just Have A "Cameo" In Captain America: Civil War: It seems obvious that Spidey's role in the Marvel movie won't be huge, but the word "cameo" was used a lot in the emails between Sony's execs. Of course, a cameo can be either 30 seconds of fifteen minutes! There was also talk of Spider-Man's appearance in this movie being used to set up Sinister Six, which IS still in development.
Spider-Man's Movie Could Include Kraven: "Kraven's Last Hunt" was suggested as a possible storyline for the next Spider-Man movie, so there's at least a chance that this could be the basis of the origin story-less reboot.
They Considered Letting Him Grow Up: Spider-Man spent over a few of his 50+ years as a high school student, but the Marvel Cinematic Universe will apparently once again depict him as a teenager. This was suggested as a direction to take the reboot in, but reliable sources have since claimed that Andrew Garfield's successor will be a teenager whose high school life is important to the stories told so this probably isn't happening.
Spider-Man Will Live In The MCU...Sort Of: As the deal was being discussed, it was mentioned that Sony didn't want Spidey's next solo film to be a continuation of the Captain America: Civil War plot just because he would be making a cameo in it. But, Spidey's new universe would "exist in a world where that story has happened" and "superheroes are now divided into two groups."
The Cameo: What does the cameo involve? Well, the plan is for Spider-Man to meet Black Widow, Captain America, and Iron Maneo, with the latter giving Spidey a new suit. That will be the Iron Spider costume from the Civil War comic book, and presumably what he wears in his first solo outing come 2017.
Spider-Man Will Join The Avengers In Infinity War: Marvel apparently want Spider-Man to appear in the Avengers: Infinity War movies that will be released May 4, 2018 and May 3, 2019. In order to make that happen, Marvel asked that Sony guarantee a second standalone Spider-Man film would be released in 2019. Marvel wants that reassurance because they don't want there to be a long delay between his solo outings.
Avi Arad And Matt Tolmach Get The Boot: This has already happened, with both men demoted from producers to the meaningless role of executive producers.
Drew Goddard Will Direct: Sony apparently wanted an agreement that would see Drew Goddard both write and direct the first Spider-Man movie, but there was no mention of this in the press release. Goddard left Daredevil to work on Sinister Six, so could there be some bad blood there?