I just bought two VFDs from Dealer Electric ( they have a new name now, can't think of it), also patronized by people in this ng.
They told me (I think) that most--or at least the ones I got-- VFDs will take either single phase or 3 phase input. The difference is, with 3 ph input, you no longer have to de-rate the VFD by
1/3. But sometimes, the rating of the VFD, anticipating single phase hookup, is * already*
derated for you.
A 2 hp VFD is not that much more expensive than a 1. My 2hp was about $250. I would go 2 just for the margin, and for the unforeseen, like using the VFD elsewhere, or changing the lathe motor, etc.
If the VFD doubles the speed of your motor (I'm not sure it can, haven't really done much with mine), you'll still have only 1,000 rpm on your lathe, not very fast for a 13", imo. You can also have your motor rewound, for two-speed operation as well, for more speed latitutde. Or put in a higher rpm motor, which would raise your lower range as well. Some re-winding houses charge very reasonable rates, while others ask for the deed to your house.
Mebbe you should put your SG motor on yer lathe!
I've been curious about the pros/cons of varying grinder speed myself. Less of an issue than say a lathe, but still might be useful for differing materials.