Dinny: 90% of the time I carry a 30-06 Handi, it's my go to beater gun. The 180gr bullet is the optamum heavy weight bullet with good range and lots of energy. The 200 and 220gr bullets are built for the 300 Win Mag and are just too much for the 30-06. Velocity is too low for good performance beyond 75 to 100 yards. Many times shots are going to be out at 200 and 300 yards, with no chance to get closer. I load three bullet weights for the 30-06. 125gr (Speer TNTs and Nosler Ballistic Tips) for varmits, 165s (Sierria BTs, Nosler Accubonds and Partitions) for Caribou, Black Bear, and Wolves. I would not hesitate to shoot a Moose or Grizzly with the 165gr either. I prefer 180gr Nosler Partitions for Moose and Grizzly. That little extra energy makes a differance.
I do also carry other guns. Next to the 30-06 my favorite cartridge is the .338 Win Mag. (Thompson Center Rifle and Ruger M-77 MKII with 225gr Nosler Partitions) Good range and stopping power when it gets there. As for the .375s I don't like them. Massive recoil and poor range. I also carry a Mauser action .35 Whelen, with 250gr Nosler Partitions.
My hunting partner usually carries a Marlin 45-70 when we are not hunting during the spring and summer. During hunting season he carries a .30-378 Weatherby. During the winter when all we are going to see is Wolves and varmints he carries a 22-250.
Now for the Ruger MKII in .338 Win Mag. That is not the gun to shoot from the bench, it is a hunting gun. Never shoot it more than three times period, till you have become desensatasized to recoil, it will hurt you if you do. It does kick pretty hard, but when hunting you never realize you have shot it when the animal falls. When I first got my first .338WM (1985) I thought about getting rid of it. It was just beating me to death (63 170lbs). Then someone told me to only shoot three shots at a time till I got it sighted in. Once I got it sighted in I only shot it for hunting. Over the years I have learned how to hold it, and how to absorb recoil. No longer a problem shooting it from the bench, especially since I use a Lead Sled type shooting rest. Im now 62 250lbs, I can absorb far more recoil now, more padding. One more thing, down around South Central (Anchorage) they get a lot of rain. I would suggest getting a stainless steel, synthetic stock, gun in whatever caliber you decide. Avoid Wood like the plague, laminated wood excepted.
Popular calibers with old time Alaskans are: .338WM, .300WM, 30-06, .375H&H. The newer guys (mostly GIs) are bringing everything you can imagine, with the .338 Rem Ultra Mag being very populer. My neighbor brought one up when he moved here. Did not last long, about two seasons. He traded it for a .300 Weatherby Mag.
Since I am no longer able to get out and chase things like Caribou, and Moose I have started shooting at long distances. I set up in a good location where I know the animals will be moving through. I shoot a .338/378 Weatherby Accumark, 225gr Nosler Accubond at 3200fps. Most shots are in the 300 to 800 yard range. My partner and I can consistently hit a 1 gal milk jug out to 1200 yards. That jug is smaller than the kill zone on a Moose or Caribou. I carry this gun for three to four days each year.