The quietest 9mm suppressor is probably going to be either the AAC TiRant or Silencerco Osprey. I know a lot of people also like the Liberty Mystic, but I'm not sure how it meters when compared to the other two (though I know its very close). FWIW if I was in the market for another full sized 9mm can, I would be buying a Liberty Mystc.
Rating suppressors for ammo is a very product specific thing. For instance, I have a 4" long 9mm micro suppressor that is definitely NOT rated for .300 Blk, but if you take a look at the Lierty Mystic, you'll see that they have approved a whole bunch of calibers for the can. IIRC FA supersonic .300 is ok as we'll as subsonic .308 and supersonic .223 as long as you're not using a SBR. But generally you can expect quite a few 9mm cans to be rated for subsonic .300, fewer rated for supersonic .300, and even fewer rated for FA. Don't shoot anything through a can unless the manufacturer has rated the can for it. When in doubt, call or email them. Most of them are great guys and will be glad to help out with any questions.