I know you're drinking from a fire hose right now, but you seem to be getting it all, otherwise I wouldn't mention what I'm about to. Since you are leaning toward VFDs, let me provide an example of the doors a VFD can open for you if you like to tinker.
Here is the thread about my 3HP VFD/3PH powered compressor. I get the performance of a 7.5HP compressor from it at some points in the operation.
That's an atypical example, but the more common examples of the beneficial aspects of VFD are:
DC braking: the VFD can ramp the speed of a spinning motor down much faster than it would decelerate if you simply removed power with a switch. This saves you time, especially on the lathe. Coming to a stop faster than you can grab a micrometer is very nice. This can be accomplished to a limited extent with just a VFD, but in order to achieve dramatic stops you'll need a braking resistor. Dramatic stops may be undesirable with a threaded lathe chuck. Keep in mind this option is available for any VFD setup, not just lathe spindles.
(Obvious)
Adjustable speed: mechanical speed ranges can be made obsolete in most/many applications. This is especially nice when those speed ranges are achieved by belt/pulley changes. I removed all the belts and stepped pulleys, intermediate shafts and such from my lathe. I have a single belt going from my motor to my spindle. I can change my speed on the fly by turning a dial. Very nice. There is a tradeoff however; with a mechanical speed reduction comes a proportional increased in available torque. With a VFD/motor speed change there is not. I removed a 1/2HP single phase motor and replaced it with a 1.5HP 3 phase motor, and rarely have a situation where I can't hit the desired speed/cutting load. This on-the-fly speed adjustment allows me to face large parts while maintaining a more-or-less constant surface speed for a nice finish which would be impossible if stopping for belt changes.
Warp speed: you can go faster than 60Hz. This comes in handy when drilling with small bits. As long as your spindle can cope with it, most inverter duty motors are safe to operate up to double the nameplate RPM (see motor MFG documentation, usually a "maximum safe speed" spec will be given)
Motor & machine protection: Many older & smaller machines (the type hobbyists usually end up with) do not come with any sort of overload protection. At least the ones I've seen haven't. Without this, if a motor gets overloaded or if a 3 phase motor gets single phased, you're likely to burn up a motor or mechanically damage your machine. The VFD will fault out in this scenario, saving your motor and maybe your machine (and shop, if fire would have otherwise resulted).
Power factor improvement: not typically a concern for hobbyists, but it can become one. A large AC motor doing much less work than it is designed for, has a horrible power factor. This can draw the attention of your utility company and result in high charges. I had a 3-month span last year where my utility company was absolutely raping me on my power bill. My kW usage was not much higher than normal, and my cents/kW was the same as it always had been, but the ambiguous line item "TDU charges" was 3x-5x what it would be typically. The "TDU charges" were higher than the charges for my kW usage. I spent many cumulative hours on the phone trying to find out what was up, never got any answer, but eventually my bills went back to normal. I suspect it was the result of running of my 30HP RPC continually for prolonged periods. I was commissioning a large conveyor panel that required 480V 3ph but barely drew any power most of the time, so i just left that RPC spinning 24/7 for a while and I think it got me put on a naughty list somewhere. A VFD has effectively as close to "perfect" power factor as possible, so you won't need to worry about this.
Hour meters: I don't know if many hobbyists track runtime and do scheduled preventive maintenance, but if wanted to, that VFD is keeping track of your runtime hours.
Inputs & outputs: VFDs typically have several digital inputs and outputs, including relay outputs and often including analog outputs. These become invaluable if you decide that you want to add functionality to your machine. For example if you want to add a carriage stop to a lathe that doesn't have a VFD, usually this would require some creative mechanical solution. With a VFD you can just mount an adjustable limit switch or proximity sensor and wire it to the VFD's enable terminal. You could wire lights to the VFD to indicate when the motor is in its commanded speed range (to indicate cutting load too high), or you could wire an analog or LCD meter to an analog output to provide feedback on cutting load. You could wire a coolant pump to an output so that it automatically turns on if the spindle is running. I could continue providing examples, but the possibilities are endless. If you want to "pimp your ride," a VFD is how you do it.
Ok I've already typed more than anyone else would read and I have people waiting to use the bathroom so I'm ending this here. Sorry for the long post. I got carried away.