Buying a good used lathe is sort a crapshoot unless you are an experienced machinist or are friends with one. There are numerous inspection points and things to look for that can mean the difference between "good" and "wornout and hopelessly inaccurate" in a twenty, thirty or forty year old machine.
If you have the resources to buy a new lathe, you might consider the Grizzley line, where they advertise one of their models as a gunsmith special. The owner of Grizzley is a rifle competition shooter, and aimed this model specifically at the gunsmithing market.
In general, your choices are: used American made iron, or newer Asian machines. There are more expensive European machines of course, but their prices generally leave out the gunsmith buyer.
For gunsmithing work, you will use the lathe for mostly threading and fitting barrels to actions, chambering, crowning, and profiling barrels. Accuracy is a function of lathe condition and setup, more than anything else. Condition of ways, headstock bearings, crossfeed and compound slides, tailstock alignment, etc all affect accuracy. This is where an experienced inspection eye is essential.
The basic lathe requirements are: 10" or 12" swing, barrel length between centers (36"), quick change threading ability, powered lateral and cross feed, miniimum 1 1/2" spindle thru hole, 3-jaw and 4-jaw chucks, dogs, centers, steady rest, rigid toolpost, tailstock jacobs chuck, etc. The more tooling the better.
Brand names include: Atlas, South Bend, Logan, Clausing, Rockwell, etc in the used domestic machines, and Grizzley, Enco, Jet, etc in foreign (asian) machines. A fully equipped 30 year old Atlas fully tooled and well cared for is probably the best buy at $600-$1500. You can frequently find them on EBay. Accessories and parts are still widely available. Lathes in this size are sought after by home machining hobbyists, and competition will dictate prices.
If you live in or near a major city, Craiglist is a good place to look. You will often see machine shops and hobbyist lathes available.
Again, if you live near a major industrial center, the surplus machinery shops will be good sources. Generally, the best buys are from individuals or shops closing down.
Where are you located?
HTH
John