For those type of distances, you can easily use a 6BR for target shooting and varminting. For hunting, my ideal would be a fast 7mm and 162gr Amax/SST/Accubond.
You could just as easily use a heavy for calibre bullet from 6.5 to 30 out of a '06 and larger case. That is not very far to be able to kill something effectively. The only thing I would want is reduced wind drift and high retained impact velocity.
Here a fast 7mm like the 7RM/WSM/280 reg and AI or 7 Mystic are ideal. A 6.5-284, 6.5-06, 6.5Rem and win mag are more then enough gun too.
As to the orig question, the 300WM is more then enough. Would hunt with 180gr SST or 178gr Amax and have at it.
Jerry