I also like the Winchester rifles, Savage makes a plethera of accurate choices also.
The main thing is pick a suitable caliber, and practice with that dude until you feel comfortable shooting at game at various distances, in various positions.
As far as a caliber goes Id start at .270 win, if elk is a possible target, and move up from that point as far as suitable calibers go. Any caliber that is suitable for elk, should also be fine for smaller game of course. And if you start to handload, the caliber you finally pick can possibly be loaded up and down for the varying size of game that you decide to go after....I also think 7mm 08, is a low recoiling option for you.
Reading literature on any guns and ammo always help a new big game hunter.
Good luck and happy shootin dude.
Thanks for coming!