I live in the western slope of the Rockies. Mountain hunting in my book includes Bighorns and Bull Elk, Sheep are at the very top of the list.
I have gone to takedown rifles, they stay safe and dry in my pack, hold their Zero. You can budget a takedown Browning BLR for under 2500.00.
A .270, .280 or 30/06 is ideal and a 22" or shorter barrel is a must( if it isn't a takedown).
Get the best binoculars you can afford and get fit....my little old opinion.