I've never hunted Caribou in Canada but I've shot a few here in Alaska. I happen to be a big fan of the .30 caliber rifles, but I shot my first Caribou with a .270 and that's what my wife hunts with.
I hunt with a .300 Wby mag with 180 gr. Barnes X-bullets so that I don't feel undergunned if I happen to run into a determined bear. The thirty caliber gives you a huge selection of bullet weights and styles to tune to your particular gun and you don't have to shoot a magnum to get the job done.
Just be sure that you are comfortable shooting whatever rifle you choose at distance ranging from 30 to 250 yds. The longest shot I've ever had to make on any animal was a backup shot on a Brownie at 110 yds. and my Caribou kills have been in the 75 - 100 yd range. There are a lot of places on the tundra where a 250 yd shot is probably the norm though.
Hope you have a good hunt