For 20A, 12AWG is fine. I think for a short run, 14AWG should be alright, but I like to oversize a little, just in case. I'm pretty sure SOOW is what I used. It looks like SJOOW insulation is rated for 300V, while SOOW is 600V. I don't think I'd be comfortable being right on the edge of the insulation rating for SJOOW.
I don't use any shielded cable for my VFDs. In theory, there is electrical noise being emitted from the wires due to the way they generate the 3 phase. In practice, it hasn't bothered anything in my garage. Even the import DROs don't seem to mind it, and they seem to be the things most people see issues with. There's also that this is a grinder. It's not something that you are going to likely be running with sensitive electronics also in use. My biggest reason for non-shielded is that it was easy to get locally. The local HD had a remnant that was inexpensive as well, so I figured I wasn't out much if I ended up replacing it.