I was just responding to a similar post a few days ago. Here were my suggestions...
I just tooled up a slightly larger 12x36 lathe. After a few months of using it, here are my thoughts.
Used all the time:
-Swiss Type test indication (0.0005") and flexible mag base. This is a must have. You don't need to spend a fortune.
-1/2" keyless drill chuck and MT arbor to match tailstock. Don't buy bigger than 1/2" right now.
-Quick change tool post (CDCO tool makes a cheap but nice one)
-4 jaw chuck. Must have for any accurate work where you must pick up existing features or requires back work.
-Basic OD turning tools and a few boring bars (I use indexable carbide, but most will point you to HSS, you decide)
-Measuring tools, get some calipers, telescoping bore gages, micrometers as big as you expect to turn (0-3" to start maybe?), and the test indicator stated above. Your work is only as good as you can measure. You don't need super name brand stuff, but I would recommend buying new, or at least buying standards to check your used instruments.
Used only a little:
-Dead center
-Live center
Haven't used and probably might never need:
-Faceplate
-Headstock center
-turning dogs
I love Shars tool company (out of Illinois). They import all their stuff, but it seems to be better quality than most imports (plus they will replace anything which doesn't meet your quality standards). They're pretty inexpensive too.
IMO, there is a a difference in buying junk, midrange, and production quality stuff. Don't waste your money on the junk, but don't go crazy on the tooling cost, unless you intend to start production runs. The nicer, import stuff works great and will last many years.