VFD

Ordering oversize is not a bad thing at all, because now you have reserve power for other items you may want to run in the future. If @gzig5 has anything to add as far as other benefits, I would like to hear about it, although I have seen firsthand the torque loss associated with the 66% or lower speed reduction. That was on large Winsmith double worm reduction mixer (treatment plant flocculator) drives with 1-1/2 HP VFD specific motors.
Being a bit oversize isn't a bad thing and our sizing software tends to build in and recommend a little margin. For example lot of customers will buy a 5hp drive model to run all the 1-5 hp motors on a machine. Imagine how many conveyors and motors are in a UPS or Amazon facility and you'll understand the benefit. Allows them to carry fewer spares at the slightly higher initial expense. I've run 1hp motors on 75 HP drives and they work fine for a low dynamic application. The current sensor feedback is down in the mud and you wouldn't do that big of a mismatch in an idustrustrial setting, but it works for the testing that I need to run. There is a tipping point for where you start to loose signal fidelity on a large mismatch, but I'd expect a 1hp to work on a 4hp drive just fine.

I wouldn't expect the speed on a lathe to be a problem unless you are running a 100yr old one with plain spindle bearings and then the limiting factor is the bearing design. On a mill, if you know you are going to be running higher speed with small diameter tooling most of the time, I'd suggest changing the pulley system or if possible go from a four to two pole motor (1800 ->3600 rpm). If you have a quality US made motor, it may live at the higher frequency settings, but they do make inverter duty motors for a reason. Regardless, I'd figure out how to add a cooling fan to the motor if you are concerned. You can spend some money on a industrial quality drive an a motor with encoder and significantly enhance your speed/torque control, but seems like overkill on a Bridgeport spindle and a lot of people make a lot of good parts with a standard VFD setup. If you do jack the speed range up, keep an eye on the spindle bearings.