It's true a heavier lathe with thicker, heavier bed and ways will have more stability than a lighter lathe with thinner bed and ways.
Like I mentioned, the Atlas/Craftsman 12" lathes are at a disadvantage in this category. It is simply much easier to do good machine work on a Clausing, a Shelton, a Monarch, or whatever. They WEIGH a lot more, and the difference in weight translates to a stiffer bed, greater rigidity of headstock, crossfeed, and compound. What is also true is that a careful craftsman, knowing the limitations of his equipment, can still do nice work.
The easiest way to aquire a gunsmithing lathe is to buy the Grizzly package. Fully equipped with steady rest, follower rest, 3-jaw and 4-jaw chucks, faceplates, centers, tool holders, and dogs, the new user is unlikely to outgrow it. However, it will also cost 2-3 or 4 times what the more modest Atlas will cost. It's certainly your choice, but you asked for advice, and we gave it.