VFD's do not need to be oversized unless you are buying a generic Chinese brand and if you are trying to drive a difficult load to start. VFD manufactures stat the output amps in both variable torque mode for pumps and fans and constant torque loads for most machines. They also have normal duty (ND) and heavy duty (HD) output ratings, as well as any de-ratings for say single phase input on a 3 phase input model, etc. You look at the output amps and make sure that they apply to the motor rated full load amps at the rated voltage and a bit of margin say 10% or more. It also depends on the load type and if it is intermittent or continuous at full load.
The GS21-23P0 I linked to previously is a single phase input VFD, output current is 11.0A in constant torque and 12.5A in variable torque. The Teco motor on eBay is rated at 7.7A@230VAC and 8.78@190VAC. There would be no reason to oversize the VFD. Most "3Hp" single phase input VFD's have an output rating in the 9-11A output in constant torque. If using a 3 phase input VFD and trying to run it off of single phase, the general rule of thumb is to derate the VFD by 50%, but it is VFD brand and model specific. The flip side is I have heard of a number of people buying generic Chinese/HY VFD's and then going up in smoke when driving difficult loads like compressors and that is even with upsizing the VFD. I would double the size of the HY VFD in that case.
