Grizzly|\asian lathes are the tools that are adequate to get the gun tinkering job done, and alot of people seem to like them.
From a machinist standpoint (I was one for years before this engineering schooling) the homeshop priced machines are absolute trash. The gear head lathes while functional, leave alot to be desired as far as the gears themselves are sometimes crap (hard to engage another speed). The apron gears on any low cost imported are weak pieces of crap, I've fixed many that were wore down/stripped. Some have a very complex electrical system made with low grade components, and are complex to trouble shoot (il admit im no electrician).
Like I said there's a good chance that it will do the job for you, as far as parts are concerned, well come models get discontinued and good luck getting parts for those.
If you want a machine thats simple, reliable with good quality components, I REALLY recommend a used machine of domestic manufacture. Some names to look for are clausing, colchester (not really domestic its made in england), southbend, logan, delta rockwell and the heavy duty modern Atlas (not the toy ones).
There are good quality imports from asia, new ones are expensive but usd names to look for are Mazak, Mori Seki and Kingston.
Theres 2 basic styles of lathes, your belt drive and gearhead, il explain the differences.
Belt drive: Very simple, shaft with a step pulley between 2 bearings (and a thrust bearing) your high speeds are direct off the pulley and low speeds are from the back gear. This whole setup is easy to repair and service. Most of the old domestic lathes go off of this drive. Cons are you most likely wont get the fastest speeds, but it doesnt really matter.
Gearhead: Complex as hell, the bigger/modern domestic and asian lathes use this. Pop the lid on a gear head and think real hard about how your going to get a gear out of there if it craps out on you, or how youl go about replacing a bearing. Saves you from having to swap over belts, and alot the the gearheads have automatic oiling (the tubes get crushed easily). The pros here are you can get a good speed out of them usually (not that 2500 rpm is needed anyways)
Size of your machine will dictate the most, the bigger the spindle bore you can get the better (within reason, dont go buying an oil country lathe
). Size seems to dictate price for used machinery as well, the bigger it is the cheaper it is, and the more of a PITA to move.
But hey I use a teeny tiny myford super 7 (another damn import englishmen lathe) for my gun tinkering (I cant rechamber full size rifle barrels, but for little carbines with a steady rest I pull it off), and pistols is a kinch. There a veeeeeeeeeeeeery nicely done up machine and depending on your needs and if you can find a used one in your area thats reasonably prices (not likely) it may fill your needs, if your gunsmithing for a living forget about it, this things for playin, not making money.
Anything made by Jet is absolute garbage, if your looking for a boat anchor in 2 years buy a Jet.
Purchasing used: If your on the east coast were there has been some heavy industry, craigslist is pretty good, as is the buy and sell/want adds. Some auctions come up and there may be something good there. If your in the west, good luck, chances are youl have to truck your toy to you and those that are available tend to to ridiculously priced. And watch out for that, people who want a kings ransom for there tinker toy.