I use to have a customer that did inner-city hunts at night with a supressed Remington LTR in .308. He was very successful. He had his supressors custom made.
A supressor will not do much in the way of sound reduction so long as you continue touse normal super-sonic amunition. If one uses
sub-sonic ammo a properly made supressor will make a sealed breach firearm (bolt action, break action)very very quiet. Quiet enough that you could literally hunt right behind a house and they would not hear the shot if they were inside.
Obviously recoil is incredibly light in a rifle shooting sub sonic ammo.
Some cartridges to think about for supressed shooting is the whisper line of cartridges. They are experts at supressed firearms and cartridges.
http://www.sskindustries.com/index.htm