Define low cost, low cost as in overall not very expensive (couple hundred $). Or low cost for a good lathe (1k-2k)?
-Jenrick
Agreed. This is one question that is super dependent on your machining skills, willingness to go and pickup the machine, and how comfortable you are in restoring a machine that is in less than running order.
First, you need to define what you're looking to machine. This is going to define what you'll look at buying.
Next, you need a very rigid lathe for maintaining accuracy over the length of a barrel plus your stock that is needed to chuck the barrel to begin with. This pretty much means big & heavy (think about 1-2ton+ in weight) machines that will be in the garage on a heavy concrete slab. Also, look at swing over the carriage and bed length. If you're machining a 16" long barrel, you'll need at least 20" between the chuck face & tailstock, so that'd be a bed about 36-48" long. Also, do you want a 3 or 4 jaw chuck? If you want a 4 jaw, how comfy are you with a dial indicator at indicating the material onto the central lathe rotational axis?
Third, you need to evaluate your skills in relation to the machine. I personally need at least an 8spd lathe with a compound post & 4 jaw chuck in order to do what I am able to do on a manual lathe ($8k-$12k new). I would like a 3 gear infinite speed lathe with definable feed rates, metric & english threading gear settings, and an option for a plug in CNC controller for some simple contouring operations ($15k-$25k new). And if you're wanting to flute the barrel, thats going to cost even more because you'll either need a milling machine or a manual third axis on the lathe to cut the flutes. Lets not even get into live spindle tailstocks as I've only seen them on the expensive CNC machines.
Finally, how much money do you have for this machine? If you're looking to buy new or a good quality used machine, regardless of age, its going to cost a mint to buy. If you have the tools & skills to, you can buy some ridiculously good machines for next to nothing because most everyone sees it as a beat to hell machine. The supervisor shop I worked in while in college bought a 48" drop saw that could handle 1" thick blades for $100. It was a **** pile when he bought it, but since he had the tools & skills to rebuild it, all he was out was another $500 to get it running. He spent $50 on raw materials and machined all the parts he needed, $250 on a new motor, and $200 on a couple reels of saw tape for making blades. Another, even better buy, was his metal working saw with integrated blade making tools (welder, grinder, and annealing tool). He got it for free and running for $150. He got it so cheap because someone had knocked it over and broke the cast iron saw table. Again, $75 in raw materials to machine all the needed parts himself and another $75 for TIG filler rods for cast iron.
Its all dependent on what you know and how good you are at turning garbage into gold.