There are a lot of good comments here so I'll add something a little different. My advice is to buy used. Look at as many options as you can, join a club and try out as many as you can, decide on some that will do the job and then look and be patient. Woodturning is an old guys activity and old guys lose interest or die off so there are always good used lathes on the market. I bought an eight month old Powermatic 3520B for $1800 about six years ago and could probably get close to that now if I sold it. Patience!
I fish, therefore I am. I woodturn when I can't fish.