R. O'Brian wrote:

There is no advantage to oversizing the VFD. Buy the 1 hp model.

You will get plenty of advice on building a phase converter. Forget it.
The advantages inherent in having variable speed completely outweigh the
possibly lower costs of a homebrew phase converter. Most of the top of the
line tool room lathes have a mechanism for infinitely variable speed
control on the fly. Once you get it, you will know why.

Randy
(VFDed lathe, mill & belt grinder)

What he said. I have a 10" lathe and a knee mill
and both of them have 1 hp VFD's. I've never
tripped them under load and they work perfectly.
A back-geared lathe with a vfd has no problem
turning 10 rpm if you need it.