The commercial static convertor contains all the above-mentioned parts plus a voltage sensitive relay that switches it off when the motor has come up to speed. They run from about $85-$170 depending on horsepower of the motor they are starting (there are more expensive ones for higher HP motors but I wouldn't use one for a large motor.)
You can spend your money or spend your time. You can usually find a used 3-phase motor for cheap for the idler. With the idler, you get much better quality power than with just the static convertor. I would not recommend the use of a static convertor only except for the lightest duty
My "idler starter" consists of the capacitor, contact switch and fused knife-blade, 2-pole switch and were about $30 all together... which also brings the idler motor "up to speed". Releasing the momentary contact switch also "turns off" the idler starter. It's a quick "1,2,3" start sequence: 1) press momentary switch energizing capacitor to third leg of idler, 2) engage knife-blade switch to turn on 220v single phase to the other two legs of the idler, 3) release momentary switch.
Every dime I was able to spend at the time was pretty hard come by so yes... I guess I did have more time than money. The idler motor was $75 (or $15 a pony... 5 HP). I take pretty heavy cuts with carbide insert tooling so everything gets a good workout. My machining is, however, "intermitent" compared to a regular job or production shop. Both machines' motors are 3HP.
My first one was a rope-start version and ran a 16" South Bend lathe but I seemed always to want to make another cut right after I switched it off... and half the time didn't because of the hassle of winding the rope and having to yank it before powering the idler. That idler motor was a larger, older 1100 RPM guy so the relatively slow rope pull would get it going. Went with the lathe when I sold it.