Take a class before you commit, to make sure you really like it. Then go as large as you can.
I have perhaps twice the money in tooling that I do in a lathe, so be prepared for the total expense.
Don't get less than a 16" swing in a lathe. You can turn small things on a big lathe, you can't turn big things on a small lathe. 1.5 HP is enough power to turn big things. Heavy is one measure of quality, as vibration is your enemy when turning and the heavier you go the less vibration you have to deal with. If you want to turn really big platters and such, get a lathe with a sliding or swiveling headstock. Look at Nova Galaxi lathes - a bit pricy compared to the comparable Grizzly or Jet 1642 but not having to deal with belt-driven spindles is a plus, as is the swiveling headstock. If Nova is too much then look seriously at the Grizzly. Stay away from the harbor freight and other micro-lathes. Or be prepared to re-buy in 6 months.
Tooling - cheap stuff doesn't last. Buy a cheap bowl gouge one time when learning how to grind it, and then buy the best gouges you can. A Thompson gouge lasted 2 years, a Hurricane gouge lasted 6 months.
You need an 8" grinder, slow speed is ok but not critical with modern steel tools. Wolverine jigs are great for learning how to grind. You can do it free-hand but you will go through a lot of steel in the process, and the results across your rools will be wildly variable. For consistent grinds its hard to beat the jig.
Spindle turning - To start out, get a 1" spindle roughing spindle gouge, a parting tool, and 1/2" spindle gouge. Bowl turning - start with either a 1/2" or a 5/8" bowl gouge, and a 1" scraper that you can grind into a negative rake profile.
Join a club, or make friends with an experienced turner. Check out the Internet - there's lots of misinformation out there, but people like Stuart Batty or Lyle Jamieson have made some wonderful videos. Get lots of books, on both technique and design. Buy a book with lots of pictures of innovative designs, like the 500 Wood Bowls from Lark Crafts - it's both humbling and inspiring! And turn - a lot - repetition is the mother of all learning.