Saxophone question?

I am an advanced guitarist and a clically trained pianist but I got turned on to Jazz while living in new orleans from 98-05 and I have decided to pick up the sax (and then that's it, no more instruments unless I win the lottery) I understand that the tenor is bigger and more difficult to learn than the alto, but it is the one most used for Jazz...should i start on an alto then go to tenor? I have been told I can't get anything but a junk sax unless I am willing to shell out 1500+ dollars...so should i rent? any advice would be helpful and if you have already answered one of my sax questions sorry for the redundancy it's just that i wasted so much money as a beginning guitarist because I didn't know what i was doing.