Grizzly has three lathes it calls gunsmith lathes. They have a couple of added features for gunsmithing. The owner of Grizzly is active in benchrest shooting, so he does have some experience in what would be appreciated. While they are typical chicom machines, the combination of features and an attractive price make them appealing for gunsmithing.
This is the 13" machine, there are also 14" & 16" machines;
Just myself, but I would prefer a belt drive machine for the better finish provided. The main things to look for are enough room through the headstock for a barrel to pass full length and 5C capability so that you have 1-3/8" through the headstock.
A Heavy 10 is an excellent machine for gunsmithing as are most 13" machine. I have a 13" Sheldon which will do anything I need. I think anything over 13" would prove too large for most, a smaller lathe would be needed for small work, and most gunsmithing beyond barrel work is small work.