I have killed about 22 caribou over the last 10 years. They are pretty easy to kill. 21 have dropped dead right on the spot, 1 took two shots because of a poor neck shot. The most premium bullet I have used is a speer hot-cor. I have used many different calibers (.243, .30-30, .30-06, .300 win mag, 7mm rem mag, and none did it better than the other) Just make sure the distance you are shooting is within your skill level and you should be golden.
They dropped quite quickly with bullets in weights from 100 grain soft points up to 180 grain federal hot cor's. But if you choose better bullets, make sure they are quick expanders, and not controlled expansion. Caribou aren't any tougher than deer, and not much thicker. Good eatin though