Is it that time of year again? You're in BC, so you have bison, grizzlies, mountain sheep and goats at your fingertips. The best all around cartridge for your purposes is the .300 Win Mag. This considers ranges out to 500 (mountain game, trajectory and energy delivery at range), effectiveness on bison twice the size of moose, grizzlies, ammo availability off the shelf, and rifle selection available in the chambering. Other cartridges will do, and offer things like less recoil if that's a concern. But you didn't ask the easiest cartridge to shoot, you asked for the best and for BC I'm convinced that's the .300 Win Mag. Four out of six clients we had show up this year to hunt BC had some form of .300 mag, in my opinion they chose wisely.
If you're never planning to chase the exciting species lesser chamberings would do fine. Would be a sad choice, you can do more than a quarter million dollars of hunting as a BC resident for the price of tags.