I don't think anyone can do more than tell you what's available in your price range unless you can specifically say you need to build X with a lathe. But, in reality, you'll either buy something that's perfect and you'll love forever, or you'll quit the hobby and never use it or want something else because now that you know what you're doing you realize you'd rather have XYZ brand something" X something".
I had a little machine shop experience, and by luck I happened on an Atlas 12x36 a few years ago very close to home. It's been great (and I love that it's 40+ years old) but now I want something more robust within the next year. Why? Because I'm now so much more familiar with lathe operation than I was, and I want more rigidity for some of the things I make. Did I know that two years ago? Nope.
So I'd say to pick something that's in your budget, use it for a few years and then upgrade if you feel the need. I've had great luck with Grizzly customer service, and this forum is a great resource. Say you spend $1k+ now. You'll probably be able to sell it for $750 or more in a few years if you take care of it and add a few simple items. That's not a bad investment.
This isn't a cheap hobby, but I could spend all weekend in my garage doing things. One of my favorite things in the world is to take a broken something from someone with an utterly lost look on their face and either fix it or make a new one.
-Ryan