Originally Posted by
109jb
In the document it looks to me as if he is turning the entire length on a taper, hence the boring head installed on the tailstock. That is one method for taper turning. If he is indeed turning on a taper then you are going to need a lathe with enough length to do this and this means a center to center distance to accomodate the barrel + the extra length of the boring head. The between centers distance is generally with the shortest centers in the headstock and the tailstock. So if you wan to do a 22" barrell, figure needing about 26" advertised between center distance as a minimum.
If you don't need to turn the whole barrel on a taper then the other operations looks pretty benign and anything that has a through spindle bore greater than 0.7" should do. This includes the 7x10/12/14 mini lathes. That will be the cheapest, but I had one and wasn't impressed. Mine was a Harbor Freight version so that may have had something to do with it, but I wasn't a fan of the 500w DC motor, and I remember the feedrate being too high for steel even with the lowest set of gears installed. I would personally step up to a bit bigger machine but if the barrels are all you are going to be turning then the 7xXX lathes might be ok.