I have been fortunate to live in an area with a huntable population of bighorns. I have also hunted thinhorns in northern BC. Many of my friends are sheep hunters as well. Seven mags of one sort or another have been the most common cartridge used over the years, in my experience. I used a 7-06 Ackley Imp. for thirty years with 140 grain partitions and they worked well. The rifle was a 721 Rem with a Hart Stainless barrel and accurizing work done by a local gunsmith legend named Bill Leeper. I also killed sheep with .300 win mag and .270 win. Scopes were just run of the mill Leupold 3 to 9's. What I learned is good bullet construction is essential. Sheep are sometimes shot in their beds and the angles are awkward. Long shots aren't unusual and follow up shots are difficult. Most of my hunts involved lots of going up and down mountains sometimes with a very heavy pack so rifle weight mattered - but not as much as a steady hold. I can never emphasize enough that the rifle set-up must be tough. You fall on it, you bang it off rocks while you climb through boulder fields, you drag it through jack pine thickets, coming down mountains with a sheep on you back it becomes a cane, it might even be a rudder if you go into a slide down a rocky slope. Fine gritty dust gets everywhere and so does moisture. In a pinch your shirttail becomes a lens wiper that grinds sand into the lens of your scope - but you don't care because a sheep just stood up on the hillside across from you. What ever you use for equipment, don't fall in love with it. I have witness too many sheep hunting partners bouncing down mountains with their arms wrapped around their special rifle when all they had to do was let it go and stop. Sheep hunting is a disease, particularly for the young and fit, as you grow old it becomes merely and obsession. Be warned.