There is a lot of good advice here. I do recommend the purchase of a large enough machine initially rather than buying a small "trainer" lathe. When you upgrade, and you will, you will have to repurchase most of the accessories over again. It is quite easy to spend as much in tooling as the initial purchase, so in my opinion, spend it once.
Generally anything fron a 9" South Bend up is adequate for gunsmithing, but I would prefer a Heavy Ten as a minimum. In my opinion, a 12" or 13" lathe is about the ideal size for the home and gunsmith shop. A minimum of 24" between centers, 36" is better.
Do take the length of the headstock into consideration, as some are too long for a normal barrel to pass through.
I prefer American made machines, and good used are available. The argument has been hashed and rehashed and will never be settled, but there is some very good information on the linked site on inspecting a used lathe and milling machine as well as just what a "worn" lathe is capable of. Some machinist web sites make much of tuning and rebuilding a lathe to four & five decimal place accuracy when, in fact, it might not really be necessary.
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