If you want to be able to hear tomorrow, I wouldn't recommend shooting anything stronger than a .22lr w/o earplugs. And a .300 mag with a muzzlebreakwould probably make your ears bleed and your eardrum pop, and be the most painful thing you have experienced in a long time. Oh and it would make you permanently deaf. So yeah stick to the ear plugs, even without a muzzle break.and how bad is the boom without ear plugs?
As for not making it jump so much, go for a muzzlebreak and a new recoil pad. Also get a scope with more eye relief than the one you have presently, because nothing makes you flinch more than having a bite taken out of your skull by a scope! Nastiest scope cut I ever got was from a Ruger 7mm-08 off a bench! Nicked the bridge of my nose and bled for like twenty minutes, but didn't hurt all that much. (that's what I get for shooting a rifle set up to fit my female cousin who is considerably smaller than I... ) Also try match ammo (Federal Gold Medal Match)
Fmsniper- nice rifles! I had a Savage 12-BVSS (I think that is the correct nomenclature for the top two rifles in your picture) in .22-250, and it was one of the best shooting rifles I have ever shot (as in I never shot a group with it that i couldn't cover with a dime, which is more a testament to its ability than to my skill!)