I have almost zero experience with suppressors. If you want to go that route get the legal niceties cleared up, pay your fees and then go get a 'quality' suppressor.
there is a goofy alternative that I found on youtube using oil filters for suppressors and an even goofier one where you use a 2 liter plastic pop bottle. Legal requirements afaik would be the same as for a real suppressor.
I have shot a lot of subsonic .22 ('standard' velocity target .22 ammo) and it is not at all quiet as far as I'm concerned.
Here's the oil can link: