It almost seems as if you are putting the cart before the horse, with all the questions about tooling. I would concentrate on a machine and learning basic skills first. With all the popularity of "gunsmithing " lathes, it is very easy to get lost in the sea of information and mis-information, generated by marketing hype, and beginners that lack experience. With that said, I been a competitive shooter for 35 years and in the gunsmithing business for almost 30 years, and in that period have chambered and fitted between 2500-3000 barrels. After doing that many, you tend to find the best and most efficient ways, and realize what is most important, what is overrated, and gimmicks that are not necessary. I also found the machines that work better than others.
The most coveted lathe for barrel work is the South Bend heavy 10", which unfortunately has been out of production for almost 2 decades. I was fortune enough to acquire one about 30 yrs ago, and it has served me well. With my business expanding, I needed another lathe, and finding another SB was proving fruitless, and with the last production price of a "new" SB @ 13K, I knew what ever I bought new was going to be an import.
There are several features or aspects of a lathe that are desirable for doing barrel work. Besides a large enough spindle bore, one is BELT DRIVE, for a couple of reasons:
Gearhead lathes have more moving parts, hence the longer headstock, and have a tendency to produce weird harmonic vibrations at times that transfer to the work piece and will affect surface finish and produce chatter. Not saying this is a deal breaker, but it's one more thing you have to learn to work around.
A belt drive lathe seems to absorb bad vibes and act as somewhat of a cushion. Typically, belt drive lathes also have a shorter headstock, which means you can get shorter barrels through them.
I had a gearhead lathe for a very short time, although it seemed pretty tight and it was OK for general purpose, I grew to hate it for barrel work, there were too many quirks to work around. The closest thing I could find that would mimic the South Bends features was a Jet 1340 BD. So, that's what I got and modified it to suit my needs. I've had it almost 16 years with no major problems, and it gets used daily.