The most important thing you can do to improve your playing is to listen to what others are doing. There are a lot of great saxophone players to choose from, find one that makes you say “I wish I could sound like them”. Don’t forget that sax is found in more than just Jazz. Great horn players have played R&B, Funk, Rock, Blues, Acid Jazz, Classical and more! You need to find a musical genre that you like and then seek out the sax players who play that kind of music.
Once you figure out what kind of music you like to play and you find a horn player in that genre of music you want to sound like, the next thing to do is get everything they have ever recorded. If they are from the time before the CD (pre-1980s), you might have to spend some time searching in records stores for old vinyl to get recordings that have been deleted. If they are more modern players, make sure you check places like the Live Music Archive and online live music sharing sites to see if you can get bootleg recordings of live playing. My most favourite recordings of the players I love to listen to are fan recorded live shows that I found on the internet. You can also check YouTube for live stuff, since lots of stuff is uploaded there as well.
Once you get a good collection of music that inspires you, now the fun begins. Start by choosing 10 to 20 songs and listen to them until you can sing or whistle the horn solos. This might take 20 times, 200 times or even 2000 times. The more you listen to the recordings, the more you listen to the solos, the more the ideas the pros are using will come out in your own playing. Once you get comfortable with the keys the songs are in, the next bit of fun comes. Now you can play along with these recordings, this is by far the very best way to learn your instrument. You might never get a chance to play live with your musical inspiration (but maybe you will) but you can certainly play with them every day of the week while practicing. I cannot stress how important this is. This is the key to becoming a better player much quicker.
Now I know what you are going to say, you can’t keep up or you sound terrible but that really doesn’t matter. Even if you are playing 1 note, if it is the right note, in the right key, then you are working on your “ear” and you are taking steps to be able to improvise. When I was first starting to play in bands, I picked 12 tunes in the style I liked. Why 12? One for each key, that way I could listen to others playing in each of the keys as we as be able to solo along with the recordings in all 12 keys.
A good one to start with is “Jazz Blues Fusion – John Mayall because they list the keys of the tune right on the CD jacket, which makes things a lot easier. It is also really fun music that has a lot of room for solos.
Many people also recommend the Jamey Aebersold play-along CDs and I would agree, sort of. These play-along CDs are good, they give you a work book that you can use to play along with, telling you the keys and such but there is just a rhythm section, no soloist, on most of them which means there is nothing there for you to hear and learn from, it is all you. While I have owned some of the Aebersold play along CDs, I prefer to play along to my favourite players. I feel it teaches me more.
Get out there and find some recordings you like. Ask around, other players, friends, search the internet. There is a player out there that you are going to like and I can even bet there will be more than one. You might even choose one that plays locally and get to go listen to them live!