Cost-wise, there isn't any point in discussing the matter when talking about used.... it's whatever you pay...
If you get a cheap DC motor, get a KB controller or similar. If you find a cheap 3P, you can get a half horse capable VFD for around $100to $150 from such sources as Dealer's electric. In fact, D E MIGHT even have a single phase VFD, but then you need to come up with a PSC motor.
Dealer's electric etc have overstock stuff, discontinued etc, so that stuff is cheap. Otherwise, those sources sell full pop new stuff as well. Make sure you know where you are on their site, and have some clue what it ought to cost as overstock "distressed merchandise".
New cost-wise, the DC motor will be the most, the 3p plus VFD may be the least, and the single phase and 1p VFD in the middle. All will be expensive-ish. DC motor probably the most because they are the most complex to make.