There are a couple things to keep in mind when you start turning.
- What will you really turn?
- How much time do I have for this addiction?
- Am I looking for the latest and greatest or can I settle or getting by?
A lathe will cost you anywhere from HF $200 - $1000 as a starter lathe. With a lathe there are a couple things to keep in mind, reliability, speed, and swing.
Reliability - Do the bearings hold up over time?
Speed - How SLOW does it turn. The larger the piece of wood on the lathe, the slower it needs to turn, especially if you are just rounding the blank.
Swing - Swing is the largest diameter a piece of wood that can be turned between the center and tailstock. Most starter lathes have swing between 10 - 14". It may not sound like it but that's a pretty big bowl.
Of the starter lathes Jet probably has the best reputation. They're reliable, take abuse, and have common spindle sizes and Morse Tapers (MT#2).
Once you've got the lathe, you can spindle turn between centers and bowl turn using the faceplate. You will need to purchase a basic set of spindle turning tools and 1 bowl gouge.
You can get away with hand sharpening using a stone or hone, but its tough. If you have a grinder you're all set. There is a lot you can do for $500, as long as you don't go overboard on big name gouges and stuff.
In addition to the AAW mentioned above, I would highly recommend checking with your local community college. They may have a woodturning class and registering there will give you time on a lathe with tools you didn't have to acquire. Alternately, you can look at woodcraft or Rockler as they often have 1 day classes on turning.