From my experience, all good information here. The Atlas-Craftsman 12X36 is a great choice for an American-made lathe. Parts and tooling are available. They sorta targeted the hobby machinist as well.
For me, it started with how heavy is it? Followed by where you gonna put it? Then what kind of electrical power does the motor require?
These are all minor hurdles. Spend some time viewing youtube topics like, "so you wanna buy a used metal lathe". If the Atlas-Craftsman sounds good, the extensive video library of TubalCain on youtube is the place to start. South Bend produced a bunch of lathes over the years as well. Both were designed with readily available chuck mounting designs and internal tapers in the head stock for collet use.
I hope you find an Atlas-Craftsman or South Bend heavy 10 that a retired machinist bought for retirement years use, got sick of the Michigan winters, and moved it lock, stock and barrel to Arizona. And there it sits.
I have a Sheldon 10X26 and an Atlas-Craftsman 618 bench top for the tiny stuff. My lathe/milling attachment uses are the same as FOMOGO above.
Tooling is where you really can spend some bucks, so, in a perfect world, your lathe would be purchased "well-tooled".
I've been looking for a proper mill forever, I've long been tired of "borrowing" a friends Bridgeport.
Hope this helps,
Steve