I've replaced all my single phase motors in the metal shop with 3 phase motors and VFDs. Either because the machines were 3 phase to start with or I wanted to upgrade them for variable speed.
I got 2 kits from these folks years ago.
They are also a good place for affordable VFDs.
If you buy a VFD used off eBay, make sure it's the 200volt class, as the 400volt class will not work unless you have 440-480VAC in you shop. Also make sure you can download the manual from the manufacture's web site, as that's needed. I've never been able to find the manuals for older VFDs from Allen Bradley/Rockwell Automation. Seems they expunge that from their web site. You want to check that the VFD will run on single phase input. I've never had that issue with any of the VFDs I've gotten. Also if you want decent torque at low speeds the VFD must be of the sensorless vector control. That may be a standard now, but when I put the first one on my lathe, it had a scalar type control, and that has no torque at low Hz operation. It was a FM50 (Flux Master 50) Westinghouse VFD (now TECO). I learned from that.