If your goal is gunsmithing that lathe is going to be a complete waste of money for you. You aren't going to get satisfactory results and you will very shortly want to upgrade to a larger lathe that is more capable. The resale value of that lathe will be VERY low when you decide to upgrade.
The lathe you linked to does not have any mechanical speed change capability (correction, it has a high and low speed gear, but is is still very underpowered for gun smithing). It is driven by a variable speed DC motor. The slower the motor goes the less torque it will produce. You will be very limited in the amount of material you will be able to remove in a pass. The flex in the lathe will make it difficult to get a clean cut.
This would be a MUCH more capable lathe although considerably more expensive:
Swing Chuck 10'Ee Lots of Extra 10 x 30 "Foot Bed Clean title Engine and Transmission works Great! The price is negotiable so just send me a message we can negotiate!
charlotte.craigslist.org
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Barrels aren't concentric, the bore very seldom goes through the center of the tube. When you thread the muzzle of a barrel you need to make the threads concentric with the bore, not the tube. The way you do this is with a 4 "independent" jaw chuck which allows you to mount a barrel off center allowing the bore to be on center. Since this lathe comes with a 4 jaw chuck that is a few hundred dollars you will not have to spend immediately to start threading the muzzle of barrels.
Assuming the South Bend 10" lathe is in decent shape you will be able to do a lot of serious gunsmithing with it for many years. You may even find that you will never need to upgrade. There are several videos available that describe what to look for when looking at a used lathe to purchase. Checking out a used lathe is almost always a nerve racking prospect for a first time lathe purchase. If the lathe passes the recommended checks I would offer $2K for it and go from there. Others can correct me if I am wrong but I believe that is the
"Heavy" version of 10" South Bend lathe which is very well respected and used by many professional gun smiths.