I am originally from New Orleans and have been away a long time and have just reccently start spending alot of time there. As a result I too have just started getting into Jazz. At the same time starting my first real budget system.
Check out www.wwoz.org 90.7. They have awesome jazz shows off old vinyl. Sounds amazing. You can stream from the internet and they have an app for you phone. I have to highly recomend this station for jazz and music all around.
I picked up and old Creek tuner with good ratings from Audigon for $75 bucks. NPR also has some good music.