Here is what I've posted on a gun board in response to a question about getting into barrel fitting. For what it's worth.
There are those who have been and will be successful by figuring it out on their own. Or maybe spending a little time observing someone else do it, or watching a video, or reading a magazine article. They are to be congratulated on their innate capabilities. However, most of us need a little help to learn and understand something technical in any useful depth. What one learns in an instructor-led course goes beyond barrel fitting. Usually there will be some time devoted to milling machines, grinders, and other machine tools. One may not own these tools to begin with, but knowing the different ways to remove metal is helpful. Shop math, characteristics of materials, heat treating, and cutting tool geometry are also covered at a very basic level even in the first or second semester. There are also the gunsmithing courses at some community colleges that should not be overlooked.
As to the selection of a minimum size lathe - I think many would say 13" X 40". While there are many lathes of that size, and some even smaller, being successfully used to do barrel fitting, they are less capable than I want to deal with. My current machine is a 15" X 50" Clausing-Colchester. The one before that was a 17" X 60" Voest. Like everything else there are trade-offs. If you want to chamber in the headstock, you need a spindle bore that will accommodate the barrel blank. Smaller lathes will likely have too small a spindle bore. Larger lathes may have a spindle that is too long to allow convenient support of the blank at both ends. Most 13" and 14" newer lathes will have a spindle bore of adequate diameter without being too long.
The advantage of a larger machine is its rigidity and ability to remove metal faster while holding tolerances and producing a high-quality surface finish. Even when taking light cuts on smaller machines, good finishes are hard to reliably obtain with carbide tooling. If one wants to use small-machine-friendly high-speed-steel (HSS) tooling, that emphasizes even more the need for basic machining skills (tool grinding in this case) which are more easily acquired through training than trial and error. Also, larger manual (non-CNC) machines are in many cases cheaper on the used market than smaller hobby machines. Those reading this thread are interested in gunsmithing but there is a very large number of people with many other interests out there looking to buy small machines for their various projects. That has driven up the price of used small machines and created a void that is being filled by low-cost Asian imports.
Both used domestic and new imports can be a slippery slope. Used domestic machines are likely to be old and often will have been used, abused, and worn out. New, low-cost imports are occasionally not assembled or adjusted properly and may have serious defects. In both cases the shortcomings might be repaired or worked around by an accomplished machinist.
Regarding new, low-cost imports - parts are usually available if the machine is currently being marketed. Their customer service is usually good and most of them are willing to send free replacement parts during the warranty period. Basically you do their quality control in your shop. That said, there are high-end Asian imports that are well regarded and much sought after. Mori-Seiki (Japan) for example, made some of the best manual machines available from any source.
Parts and accessories for domestic machines can be a formidable challenge in terms of price and availability. This is also true of British and European machines.
What does one do? Ask yourself - "Do I want to be in the machine tool quality control / repair business or do I want to be in the barrel fitting business?" Assuming it is the latter, then consider the following:
1. Patience. Search and research. Read. Go to school. Monitor this and other machining boards. You'll pick up more there about metal removal than the gun oriented boards. Subscribe to Machinist's Workshop and Home Shop Machinist.
2. Make sure you get all of the machine-specific items you'll need in the initial purchase. Never assume that you will be able to find accessories that are unique to a machine after the purchase. Besides, accessories are almost always cheaper when part of a package. Even if you get all the machine-unique accessories in the initial deal be prepared for tooling purchases. Items like chucks, live centers, tool posts, tool holders, etc. are not cheap if they are of good quality. I recently purchased a Buck, 6 jaw, Adjust-Tru chuck that cost more than some people are willing to pay for the lathe itself.
3. Get ready to spend money. Even the best of deals are likely to cost more than you thought probable. This is not a place to go cheap thinking that with a little fixing up, that baby will be a sweet machine. "A little fixing up" on a machine tool can quickly exceed the price of a comparable one in excellent condition. This is where patience comes in. Look, look, look, and look some more. Hold out for a good machine whether it is a good new one or a good used one. I spent nearly four years looking for my second lathe (the Voest). Even at that, a better machine became available recently and I bought it. My very first lathe was a little Logan 10" and it was not suitable for barrel work. I sold it and it waited 12 years for the space and wherewithal to start shopping for a proper machine. Monitor e-Bay. I'm not suggesting that anyone buy a machine sight-unseen. But you will get an idea of what is out there and what prices they are commanding. Look around used machine tool dealers, but be very, very careful. Many of these guys are like the stereotypical used car salesman.
If you are actually in business, then you need the capital to buy the right stuff and you cannot wait for the deal of a lifetime. That's another matter. You'll just have to do a cost/benefit analysis like you would for any other major purchase and go from there. But educate yourself on the true costs and the true benefits. It's easy to get caught up in the shopping for a neat machine. If you are going to do it right it is serious money. Make your choices wisely.
Remember a couple of cliches: CHEAP, FAST, GOOD - pick any two. And, if you want it bad you'll get it bad.