My out-of-box stock Ruger M77 MK1 shoots 165 Hornady SST bullets over 60 grains Reloader 19 very well. I like SSTs for thin-skinned game. It will also shoot a 180 Speer Hot Core over 60 grains of Reloader 22 quite well.
But you don't own my barrel so take this advice with a grain of salt.