Re: Sheep cartridge?
If you don't have an outfitter picked yet, the outfitter I went with was great. His name is Mike McCann and he outfits in the Brooks Range 100 miles or so into the artic circle. One of the big pluses for his outfit is horses. It is one of the few horseback hunts available up there as it is so hard to get the horses, feed and such like into the hunting area. Your actual hunt will be done on foot, but when it is time to change drainages to new area it is sure nice to have a horse to ride and one to pack your camp gear.
I'm not sure what he is charging these days, I think it was about 10,500 when I went 5 or 6 years ago. He also does combo hunts of sheep and griz. I don't have his info handy, but let me know if you are interested and I will look up his phone, email, and web info.
On the rifle, I carried my 338RUM for mainly the reason Phorwath mentioned. I wanted some "horsepower" if we had a close encounter with a griz.