The ideal motor for an inverter will have class F insulation on the windings it will tell you what class of insulation the motor has on the data plate, there might be a few that don't but 99% do
If you are going to use the machine non stop it could impact the insulation, but I have had quite a few that ran many hours with no problems, and are still running fine
Also you don't want to go below 20 CPS running the motor, or it can pit the bearings, but that is fairly rare and it you do it would be a good idea to install an Aegis ring to ground the shaft to the body of the motor to stop any pitting
If you find a 3ph machine at a bargain I would go for it. I did many times and have yet to get bit.
One other thing, some people will tell you you need to go to the next higher HP rating on the inverter, unless you like to waste money, just get the appropriate size, and sometimes you can get by with a smaller rarted inverter if you size it by amo draw, the motor rating it kind of a guide.
All of what I posted was taught in classes by Westinghouse/TECO, Square D, Emerson, Allen Bradley, ABB, Baldor, etc