You might look into a good muzzle break as well as a new recoil pad for your Savage. Just get a thread cap for hunting. For bench shooting a slip on pad, strap on shoulder pad or lead sled may be worth trying.
If you opt for a military semi auto look for one that can be fitted with a recoil pad, many have solid butt plates. Aftermarket pads are available for some but they may increase length of pull. A wood stocked rifle can be fitted with a recoil pad, just be sure it doesn't destroy value of the rifle. There are also muzzle breaks available for most military rifles with threaded barrels that will replace the flash hider.
For use in the field take into account the weight of a military semi auto (most are about 10 pounds) if hiking much distance. If you'll want a scope be sure there is a reliable mount available that doesn't cost a fortune and require an expensive cheek pad. Many battle rifles shoot 2-3 minutes of angle as built (some much better) if you need MOA for hunting do your research before buying one.