Well, in my 52 years of deer hunting, I figured out that a reasonably powerful caliber beats a .22.
I started out with a .257 Roberts, fine deer caliber. Bought a 7mm Remington Magnum to have something with a little more pop for if i got to hunt Elk, which never happened. It kills deer pretty dead, though, no worries about blood trailing. Opens a big exit wound and they usually bang/flop anyway. I now have a nice little Remington M7 in .308 that gits'er dun. Recoil? I shoot 10 gauge on geese, the 7 don't bother me at all, and I've fired up to .375 H&H magnum without hurting myself. Recoil is a non-issue. If you can't handle the recoil of a .243 Winchester, you probably got no business hunting deer IMHO.
I've taken a 250 lbs hog with a shoulder shot using the 154 Tula in a SKS. Yes, it will fully penetrate any deer that walks. I mean, it fully penetrated that hog at 70 yards. It's a decent hog caliber. I'm kinda wanting a mini 30, but the SKS works.