If you do not reload I would go 308 over 257R. I use a 7-08 with a MR barrel in a light B&C stock. Nice and light and a great shooter. I would also consider 6.5 creed.
There is a big difference between handgun and rifle round in regards to the bullet being pushed back into the case. In handgun ammo, like the 9mm, if the bullet is pushed back into the case pressure can/will be increased and could damage the gun and shooter. This is not a problem in rifle ammo...
I switched a 300 RUM barrel at just over 1000 rounds. it was still very accurate but I went to a SS barrel. Gunsmith scoped it and said it was still good.
My last two trips for elk have been on general tags and I hunted the wilderness with an outfitter. We saw elk, deer, moose and grizzly bears and of course beautiful scenery.
https://www.midwayusa.com/product/1001690098/
https://hsmammunition.com/low-recoil/
remington.com/ammunition/centerfire-rifle/managed-recoi
These are another option to consider