For pocket watch cases and metal spinning in general I would personally go with a wood turning lathe. For this type of operation you need a lot of torque and power. High precision is less important. A wood lathe with enough power to do this will cost far less than a metal lathe with enough power. One of the favorite lathes that metal spinners use is called a ONE WAY. This is a high end wood lathe but a far less expensive wood lathe will also work.