You would want a VFD if you didn't have 3 phase in your shop and the machine motor was three phase. The VFD is the cheapest way to achieve 3 phase from single phase. So you set the manual variable speed at max and use the the logic circuit in the VFD to turn the machine on and off and vary the speed.
Cheapest? Maybe not. I put together a rotary phase converter to run my 2hp Bridgeport for a total cost of around $40 - and most of that was for the twist-lock plug and receptacle!
Of course, to do something for that sort of price, one has to have a free or nearly free 3-phase motor of suitable size on hand. I picked up a 3hp 3-phase motor out of the scrap bin; it had been scrapped because the front bell housing was cracked and split. I used a couple of clamps to hold it together and tested the motor - the bearings were a bit noisy, but overall it ran fine. So I tig-brazed the bell housing back together, and have been using it for many years now as the heart of my RPC.
One could stop there, just using a spare motor and starting it using a rope - but of course I wanted more convenience. I talked with a neighbor who does HVAC work and was granted unlimited access to his scrap pile, full of transformers and contactors and capacitors - I was able to get everything I needed to put together a starting circuit and balancing capacitors, and the only thing I had to add was a couple of push-button momentary switches (a few dollars from Amazon) and, as mentioned, the twist-lock plug and receptacle (maybe $25? $30? something like that).
I built an enclosure out of scrap plywood, and voila - my RPC has been working flawlessly for many years now.
www.northamericaphaseconverters.com
