If I'm understanding correctly your criteria is a rifle capable of taking deer, hogs, black bear 800-1000 yards and any game species in the states would be nice, light rifle and no muzzle brake
and not much recoil.
A light rifle and mild recoil can vary quite a bit from one individual to another. For me light is less then 10 lbs including scope and mild recoil would be no more than recoil similar to 308. So based on my individual preferences I'd be hard pressed to find a cartridge that would be capable of taking deer, hogs, black bear 800-1000yards efficiently.
As an example a 300winmag IMHO would be minimum cartridge...maybe, some would say yes and others no...but even then your talking about recoil that is quite a step up from a 243.
I guess what I'm trying to say is somethings got to give in the equation but, I'm sure others will hopefully jump in and offer their input.