What I use kind of depends on what I used last and what type of hunting I want to do.
Deer: Rifle for stalking could be: 1894 Marlin .44 for or a G2 Contender carbine in 30-30. Might also use a Contender 10 in. .44 handgun or a Ruger BH in .44. Would not carry both a rifle and handgun.
Deer off a stand: Rifles: Pre War M-70 in 30-06, my go to gun, or the G2 Contender 30-30, or a custom commercial mauser manlicher in .35 Whalen. Have used my Pre 64 M-70 in .338 just to see if it would kill a deer, it did! LOL
Handgun off a stand: TC Contender 14 In. 30-30 or the Contender with the 10 In. .44 mag, BBL.
Elk: the .35 Whelan or the .338 mentioned above with preferance to the .35 because it is lighter and handier with a 20 in BBL and packs a punch, on both ends.