A Nosler Partition would be my first choice, because I don't think there is a bullet that would be more likely to work at all ranges with all kinds of shot placements (through shoulders, behind the shoulder, raking shot, Texas heart shot).
Bullet would be my last worry or close to it. I'd want a rifle the was DEPENDABLE in all kinds of weather, a bomb proof scope and mounts and I'd spend a few hundred rounds shooting ground squirrels with it. About 7 1/2 pounds would be the right weight, light enough to carry up the mountain but heavy enough to settle down when you are winded.
The three places I have hunted sheep (ewe tags) are also places I hunt mule deer and what works on one will work on the other.