You will need to check the frame motor size dimensions, but I would replace the stock single phase motor with the Marathon 2Hp E467. The motor space is very small, so standard 145 frame TEFC motors will not fit, you need a TENV. Alternate 2 Hp motor is the the Marathon BlackMax and BlueMax Inverter motors, they have a small encoder shaft on the rear of the motor that needs to be cut off. The pulley size depends on a number of different factors, the E467 has a usable speed range of approximately 20-90 Hz, maybe 100, so for a single speed you need something like a 3.0-3.2" pulley going to the larger headstock pulley. The Y526 and Y551 I usually use 20-125 Hz running a 2.4-2.7" pulley going to the larger headstock pulley. You can measure the pulleys and do the calculations, but I usually work it out so at your maximum Hz, your spindle speed in high gear is ~1800 RPM. The sock motor has a 3/4" shaft, the Marathon motors listed have a 7/8" shaft.
The Gates Tri-Power belts seem to work quite well, I have had no detectable belt debris spinning off since I installed them a few years ago. The notched belts work well around smaller pulleys.
I would buy a decent VFD for the lathe and run it in sensorless vector motor control, you will need a braking resistor.