If elk is part of your normal hunting a 308 with 165 grn accubonds is what I built at 6 lbs with scope. It will give you a little more assurance with quartering shots than the smaller calibers. In my opinion. It's never failed me. I've not had any recoil issues without a muzzle brake.
I've had a browning A bolt for about 20 years. It's been lightened to 7 lbs with scope and muzzle break . The 200 gr. Accubond at 2950 fps. has taken every thing from antelope to elk. I love the 325 WSM. With the 200 grn bullet It's everything a 338 WM. is.