Here in the free part of America we are not encumbered with all those ammo or magazine limitations. For hunting near fields where I have a longer shot opportunities I use a Ruger M77 MKII All Weather Stainless in .30-06. For close in work in the woods my favorite is a 16 inch barreled Marlin 336Y in .30-30, or a Rossi model 92 saddle ring carbine in .357. Both have been meat getters.
Once I get meat in the freezer I like to transition to fun guns like some of my mil-surp rifles. I've taken several with a M1 Garand and a M1 carbine, one big buck with a Lee Enfield No4 MKII in .303, and a couple with my Russuan SKS.