My recommendation ... start with a good quality mini-lathe to get your feet wet. The Jet 1220 is a great machine with plenty of power if you try your hand at a bowl, or something, but won't break the bank. It's also built well and if you like turning and decide you want a bigger machine, you could actually keep it around too.
Just a warning ... the lathe isn't the expensive part of turning --- it's the tools and accessories. You'll need some chisels at the very minimum, and more than likely you'll also need some of the following: grinder, sharpening jig setup, drill chuck, sandpaper, 4-jaw chuck, faceshield, dust protectors, more chisels, and wood (though the best kind is usually the free kind)
Good luck and if you need any ENCOURAGEMENT, I'm always glad to help. I work in both the flat and round, but really enjoy turning. I've only been turning about a year and am still a rookie ... but I have two lathes and an ever-growing stash of accessories and free logs!