Never gone after goats or sheep, but I've hunted in the lower parts of the rockies. I've got this advice:
1) Glass: Get good glass and practice actually systematically covering the areas you are glassing. There are various methods that work. 10 power binos and a tripod with adaptor are a potent combo when you don't want to bust out the big glass. For judging sheep you'd be well-served to get a GREAT spotting scope. For long sits have a bag that you can weigh down the tripod with rocks for stability.
2) Fitness: once a solid base level is achieved, you are probably better served by rucking really really heavy once a week rather than lighter more often. There's a good podcast to that effect with The Hunt Backcountry Podcast. That's based on results from fit, military-aged men. YMMV.
3) Shooting: practice shooting in the wind, in adverse conditions, to the ranges you'd expect, from improvised shooting positions.
4) Discomfort: practice being uncomfortable on your weekend practice runs. My (serious athlete) buddy did a 10 day mountain goat hunt and lost 30 lbs. Another friend spent 10 days on the mountain trying for goats with a long bow and spent almost all of it in his tent because of weather. Mental prep will go a long way towards motivation and endurance.
5) Gear: less is more. Exo Mountain Gear has resources on their website, including a whole slew of "what's in my pack" from experienced hunters. Check it out. Don't ignore advice from backpackers who have their own innovations, ie some of the lightweight backpackers don't use stoves anymore they just "cold soak" their Mountain House for 6-8 hours. Ew, but light weight!
good luck, I'm totally jealous!
the hype of lightweight can go too far. we have seen in pyrenees and alps people that has been too far for that. no extra layers no tuque or no gloves when bad weather is hitting you you want the gear that can handle it and of course a gear that is proven by your own experience. internet experts are expert on internet and while on the mountain you will not be with them and your experience will be yours not them ...
i can tell you than a warm meal or coffee or chocolate can make a big difference. do not skype on a way to get warm meals ...