are you looking for subsonic suppressed hunting?
or supersonic suppressed hunting?
in the case of subsonic suppressed... the 300 blk is probably going to be your winner. with subsonics it comes down to 1000 fps (give or take a few fps of course) to stay below the sound barrier so in that realm - so the heavier you can go the better. big + heavy = penetration. The other factor to consider is efficiency. in both of these realms the blackout wins. and if you want to go with a bolt gun... you can go stupid quiet too by playing the powder game while handloading.
bullets that expand that those speeds are going to be relatively limited and pricey. But very few good hunting bullets are going to come cheaply. Look to company's like Lehigh defense, maker bullets, or blackoutbullets.com for some good choices in that realm.
alexander arms is also working on a subsonic expanding HP option as loaded ammo, but no word on a projectile only release date.
if you're looking to do supersonic suppressed - just screw a can on the front, verify your POI shift (if any) and go at it.
HTH!