No question about it. You need a bolt action .308 Winchester, in either a Remington 700, a Savage, a Ruger 77, or one of the newer Winchester model 70s. Don't worry about it kicking hard. If your rifle has a monte carlo stock, and a high quality (NEW) recoil pad (Decelerator, or Pachmeyer or KickEez) then recoil is simply not much of a factor. And, ammo is universally available.
The reason your .44 Mag carbines kicks is that it has a straight stock, with no drop, and a small comb, and no cheekpiece to anchor your face against. Yea, it probably kicks like a mule, especially if you are sitting behind it from a bench. The .308 rifles outlined above will push back, but it won't hurt like the .44 mag.
I agree with others. You only need one good shotgun, a 12 gauge with perhaps two barrels (a slug barrel, and a 26 inch or 28 inch barrel with interchangable chokes.)
You could easily get by for everything (except large grizzly, but who cares?) with the following:
1. A bolt action in .308.
2. A bolt action in .223
3. A Ruger 10/22 in 22lr.
4. A 12 gauge shotgun, as described above. (Either a pump, if you are sure you won't short-stroke it, or a very high quality semi-auto, such as a Beretta, with a synthetic stock.)
These will accomplish EVERYTHING you need, using the most commonly available ammo in the world.
If I were able to add a 5th, it would be a Marlin 30-30 lever, or maybe the Marlin .44 lever, as a close up tactical gun and all around handi-gun.
Just my opinions.
Mannyrock
Regards, Mannyrock