Based on the Marvel Previews #8, April for June 2016, I'd say you need to pre-order the following books in order to keep up with Spider-Man.
Amazing Spider-Man #1.6
- Cover By Giuseppe Camuncoli
- Variant Cover By TBA
Amazing Spider-Man #13
Amazing Spider-Man #14
Marvel Universe Ultimate Spider-Man: Contest Of Champions #4
Spider-Man #5
Spider-Man/Deadpool #6
- Cover By Mike Del Mundo
- Captain America 75th Anniversary Variant Cover By Adam Kubert
Spider-Man 2099 #11
Spider-Man & Silk: The Spider(Fly) Effect #4 (Of 4)
Spidey #7
Timely Comics: Web-Warriors #1
Web Warriors #8
Reprints
Amazing Spider-Man: Amazing Grace TPB
Amazing Spider-Man: Worldwide Vol. 2 TPB
Luke Cage: Avenger TPB
Marvel Firsts: The 1990s Vol. 2 TPB
Spider-Man: Brand New Day -- The Complete Collection Vol. 2 TPB
Spider-Man: Clone Saga Omnibus Vol. 1 HC
The Uncanny X-Men Omnibus Vol. 2 HC (New Printing)