I'm thinking of buying a saxophone, what is the best option for me?

I'm 17 and have wanted to play the saxophone for quite a long time now, but I'm not too keen on having lessons. I can read music and I play guitar/piano. I'm self taught for guitar for 3 years and self taught for piano for 5 years, but I'm pretty good. Could I get away with learning the saxophone independently? If so, what would my options to get a cheap (preferably tenor) saxophone.