RE: big horn expidition
Sheep hunting is arduous young man, and drawing a tag in a Western state for Big horn is tough to say the least. If you just want to go though, you can get an unlimited tag in Montana. Also, you could simply purchase a hunt. This might cost roughly 30,000 per hunter, and I'm not kidding.
Realistically for the common guy, you have to put in for bonus points in several states for many years before you draw a tag.
As far a caliber suggestions, anything from a .270 on up would be okay, if you use 150's in the .270.
Good luck.