So much would depend on where I was. I'm going to assume I was looking at going up into the interior where I'm from.
Given the choice of anything legal to own (no full auto, short bbl rifles etc):
12GA Rem 870 in Stainless with as little bbl and as much mag as I can handle. If I had to stay alive and had to have only one firearm - this would be the one.
375 H&H Magnum in a Winchester Model 70. Open sights, no optic. Also in stainless.
17HMR Rifle - any of the nicer makes in a bolt action with a premium optic also in stainless. Mmm @ tasty rabbits / grouse.
257 WBY Magnum in a Mark V Ultralight for a walking gun - nothing less than the best optic I could afford to put on it. Food - getter at range, and pelt getter with head shots.
Revolver in 357 - S&W. No .44? No - the things that can kill and eat you in AK are better dealt with via the 12ga.
Of what I have:
12GA Rem 870 Wingmaster with 2x bbls - 28" VR plus a short smooth bore. Grouse are on the menu
- that or one of my Model 12s. Finest pump-gun. Ever. Period.
7mm Rem Mag Ruger RTS with VX-III. I no longer live up there so I don't own a heavier rifle at this time.
Walther P22 extended bbl - Rabbit, anyone?
.223 Rem 700 Varmint - again a food and / or pelt - getter.
S&W 686. As above. This is a general purpose sidearm that's controllable, reliable and TOUGH.
If you do get a chance to go to AK I can safely say I've seen all the firearms listed used in the field to good effect on the species they were intended for (also read - legal for) - or as a survival tool. If it can freeze - leave it home at. If it isn't silly-reliable and SIMPLE, leave it at home. If you like it's firepower but don't shoot it really well - leave it at home in favor of a lighter caliber. And practice
By far the best weapon you can take anywhere is your alert, focused mind.
I've seen some of nature's greatest work there, from killer whales feeding against a seaside cliff to the caribou herd migrating across the tundra. If you go - take good care of it for all of us, and yourself.