When I finish my morning coffee, I'll go back to programming the VFD on my metal lathe. I have a high end, Canadian made, General 26020 wood lathe. It has a factory installed VFD, but it still uses belt changes for the speed ranges. Don't think I'm rich, I got it at an auction. I bluffed the other guy out.
Since a 3ph motor would be your first install, it's also the simplest to understand and find. Ideally, a new motor that's tagged VFD ready. This involves heavier wiring and better cooling. A quality industrial rated motor should have these anyway. I found a used Baldor . I set my motor frequency range at 30Hz to 90Hz . At lower speeds, the fan is also going slower . Under load the wires are going to heat up. How many mini-grinders have you fried cutting ? I have done in a couple of Walters over the years.
A VFD is is black magic, at least to me. But industrial VFDs are part of the automation revolution so are geared to it. They have extensive programming options for flexibility. Every TV I have bought is less and less intuitive.The programmers can't help themselves, more features you know. And it's really simple to them. From experience, a quality consumer grade, easy to program VFD would certainly be my suggestion.
I hope this helps you, your little mill is well worth it.