RE: Quietest deer gun/caliber
put an ear plug in 1 ear closest to the barrel end, ie your left ear if you're shooting right handed.
or electronic muffs.
or 2 ear plugs, they make them on a string so they can sit around your neck.
See if a silencer is legal in your area..., I read somewhere that in many states they're legal, which there ya go if that's the case!
If not, I think something like a 7mm-08, .308, .243 is your best bet.
What am I thinking? a .30-30 is probably the way to go! I tend to associate less powder/case size with less noise, perhaps I'm wrong in this thinking, but if that's the case, a .30-30 would be perfect, and certainly will get the job done out to 200 or 300yds now with those new hornady 160grs.
A muzzlebreak will increase muzzle blast/noise.