I recommend a 3-phase motor, VFD combo. An industrial duty TEFC motor can often be found on eBay for cheap. Recommend automationdirect.com for a VFD. They have good prices and excellent tech support. A sensorless vector capable VFD will cost a little more, but will give more low speed torque.
On my Jet 13x36 belt-drive, the original motor pulley had a larger bore than the new 2 hp motor shaft. I made a sleeve and a stepped key to accomodate the pulley bore and the different keyway size. The only other mod was redrilling and tapping the motor mount plate to match the new motor's mounting bolt pattern. It all came together without a hitch and has operated perfectly for 17 years. I have never moved a belt on the lathe since. Speed range is from a crawl @ 5 Hz( power tapping, spring winding) to 1200 RPM @ 120 Hz. I couldn't have asked for more.
RWO