Having been a pro hunting guide for years, I carried a Ruger .44 in a shoulder holster. However, the chest rig is much handier to either hand and out of the way for a rifle sling, or pack, or??? I've killed deer and elk with it at 50 yards or less.
As for rifle, I have a 30/06 with a Brown Precision stock and it has bagged many large animals. I also have a Brno 375H&H Mag that has accounted for a number of african animals from as small as the wart hog, Impala, springbok, to the large game like wildebeest, hartebeest, Kudu and Cape Buff. It works well from up close to out as far as 500 yards. However, I limit my shots to 200 yds or less and get consistent one shot kills with whatever I am using. Weight is an issue but if faced with a big bear, that weight will be inconsequential and I want the biggest damned gun I can shoot well. The 375 is a solid recoil gun but not unmanageable. Just don't shoot it from a bench or kneeling lest you get a scope kiss!
The caribou is a relatively narrow animal and the .30 cal is almost overkill. So, the 375 is the same. However, when you go up for moose or bear, the 375 is great. Keep in mind, it doesn't matter what caliber you use if you can't put the shot where it needs to be. Shot placement is the key regardless of caliber.
Semper Fi
Rocky