It's almost a given the new Spider-Man film's going to be a reboot. That said, I think they'll discuss his origins in Civil War—where he's likely to first appear. Then, once his standalone film comes around, they can jump right into him kicking ass as Spider-Man, rather than dealing with his origin story.
I think there's a good chance that, if they cast Peter Parker/Spider-Man quickly enough (without doing the character a disservice, obviously), they can film a quick scene where Peter gets bitten by a radioactive spider to add as a post-credits scene to Age of Ultron. It wouldn't be unprecedented, considering the shawarma scene from The Avengers was shot after the film premiered.
Then, since we'll know how he got his powers (radioactive spider bite), Civil War can deal with his character deciding to become a superhero just like his idol, Captain America. It works out almost too perfectly to not be what they're currently planning.
I also brought this up on another forum I frequent: Since all signs point to Spider-Man being featured in Civil War, my guess is that they've had two scripts for Civil War all along—one including Spider-Man, and one without. That way, if Marvel would've gotten the rights, they could've featured Spider-Man without any heavy editing, and, if they didn't, well, there would be nothing lost.
I think this opens up so much for the MCU.