That's not very much $. You might try for something used. My lathe is the most expensive machine in my shop (just under $5000). Just the cast iron legs alone were $900, and that was 10 years ago. You can make your own hollow legs and fill with sand.
Length is probably one important characteristic. Heavy is good.
220v is better than 120v. Serviceable/replacement partsNice to have. I don't have a swivel headstock.
I have variable speed. It adds to the cost but is a very nice feature. To keep costs low you may have to go with a stepped pulley arrangement.
Reversible is nice to get a nice smooth finish. I wired-in a reverse switch and saved $100.
large gouge bowl or small gouge parting tool skew various scrapers
Sorby is very good. I have no complaints about their handles. A starter set of quality turning tools might run about $600. You will also need sharpening stones and tools.