Big Boy 1...I am admittedly not up to speed on the vfd's. I've read a lot about them on this forum, and I know they are favored. Having said that, they are relatively expensive. I have two three phase lathes and one mill in my shop. I run all three from the same rotary convertor. I built this convertor from surplus parts for about thirty dollars. the largest purchase will be the motor, and for your needs, I would suggest something in the 2-3 HP range. I admit that I had some of the required parts lying about...but if you purchased the entire thing I think $100.00 should get you all the way home (buying surplus). There is plenty of information available on different designs, but they are all pretty easy, and should be do-able for someone with a limited electronics background. My unit has performed admirably for about 15 years now without so much as a hiccup. I've read all about balencing the leads etc. and I did some of that... but the main thing is to use plenty of capacitors since any balancing will only be balanced for a specific load. For all of my purposes, I don't feel that the balancing is all that critical. My single convertor will run all three machines either singly or all at the same time, and given my success and the cost factor, I'd be hard pressed to recommend anything else. Dont be intimidated by the "electronics, it's really not much more than a single afternoon project. Of course, you can spend additional time and money "prettying it up", but you can get up and running quickly and cheaply.
For both your lathe motor and the convertor motor, there's really not very much to go wrong with them. A quick check of the bearings should probably tell the tale. If it rotates smoothly and quietly, your probably good to go. As for additional noise, mine is negligible. In my shop, with everthing turned off and nothing making noise, you have to "listen" to make sure you aren't walking away and leaving it turned on. Go for it!
There is no shortage of experts, the trick is knowing which one to listen to!