Reddit reviews Rubank Elementary Method - Saxophone (Rubank Educational Library)

In terms of horns, you should go with which one captivates you the most. For me, the tenor is remarkably close to the human voice and it feels more personal.

Once you get the horn, you'll obviously have to run through fundamentals. There's a good book in our sidebar called The Art of Saxophone Playing which I highly recommend you read through. I also suggest you grab a copy of the Rubank Elementary Method Saxophone to work through to build up some technique and understanding. The Basic Jazz Conception in the sidebar is also a great resource to build technique and work on jazz fundamentals. After you get going, you're going to want to start transcribing (I suggest starting with Young, Hawk, or Webster) as you'll want to begin learning the jazz language.

Also, I highly recommend that you get a good teacher (in your case someone specialized in jazz) who can keep you pointed in the right direction.

The Rubank Method books are a great place to start. Some may suggest Essential Elements and Accent on Achievement books, but for independent study I wouldn't bother.