OP's original post makes it hard to guess what type of sheep hunting, where it might take place, or how much of it he plans to do. Sheep hunting is not the same everywhere, nor especially for other exotic sheep species outside of North America.
Based on my very limited experience hunting Rocky Mountain bighorn sheep, I would have to say that I personally would not even consider carrying a 10 lb rifle. And I would rather have a longer barrel (22-24 inches) than a short-barreled blaster.
When I miraculously drew a sheep tag, I was able to plan on having a DIY hunt. Which turned out to be a truly wonderful experience! I was fortunate that I lived where I could do that, and that I was young and strong enough to pull it off.
The first thing I invested in was some really good glass. Meaning a top of the line spotting scope, and top of the line binoculars. That is something that I have never regretted doing. Great glass is super important when hunting sheep!
The second thing is that I imagined long range shooting at sheep requiring was a super accurate rifle and a big scope with lots of Xs. That turned out to not be the case at all. It could have been, but it was not the way it came down. I ended up shooting my ram at a distance where I could have done it with an iron sighted .30-30. But my rifle could have made the long distance shot if needed. I would not have risked my rare and valuable sheep tag on a super long distance shot.
My sheep hunt involved a lot of hiking, in steep terrain, at high elevations, for many days. I carried that rifle every day, along with a day pack, while hunting out of a small tent camp somewhere on the side of a mountain. At the beginning and end of every day, I was sitting down and using my glass to look for sheep. Good glass made it a lot easier to evaluate what I could see.
You never know what your sheep hunting experience will turn out like. Consider that it might be different that what you first imagine. Be flexible in your thinking and planning. However good glass and a not too heavy rifle would be a good place to start.
- Wyowind