This is a topic that could be broken down into many sub-topics and go on for a long time. Way too much about this topic for one post.

My base camp where I am working in the Andes Mountains is 14,500'. I would like to offer the following from experience over the years as a starter:

Boots: This is the number one piece of equipment. Socks are number two. From experience, do not go less than a medium weight boot and if you are in the rocks
much of the time, a good heavy-weight boot should be considered. Socks need to be top-shelf merino wool socks and don't be shocked to spend $30 or more a pair for the right socks.

A mistake in this area, specifically blisters or loose, unstable boots will ruin your trip. The boots need to be well broken in. I wear mine daily for several months before working my way up to longer hikes. When I go to Peru, I am positive I'll have zero boot issues with the preps made beforehand and so far, so good. For the 2020 trip, I will be upgrading to heavier boots as it will be 100% in the rocks this time where the medium-weight boots are border-line.

Cotton kills: No cotton, ever, in the mountains. Especially underwear. It gets cold and weather changes come fast in the mountains. You can have sunshine, rain, and snow in the same day. When you get wet, and you will, you need clothes that respond accordingly. Cotton is completely miserable in wet and cold conditions and it can kill you through heat loss. Think wool and synthetics.

If you are in an area that is hot, like the dessert, cotton can be quite comfortable and would be a prime choice.

The equipment choices are endless. If you have guides, horses, and folks to carry your stuff the choices are easier to make. If you are carrying your own gear, choose wisely.

Optics trump the rifle choice. Optics should be your costliest hunting specific gear. If you choose poorly in this area, you will ruin the trip. Do not skimp on the optics. Consider a fixed power scope if this rifle is for mountains only. Like a 6x42 with a German #4 reticle and made somewhere in Germany or close by.

IMO, it is rude to carry anything other than a control round feed rifle in the mountains like the Mauser 98 and its variants like the Winchester Mod. 70.

Caliber needs to be flat shooting and have the capability at longer distances. There are many good choices.

Shooting sticks are a necessity with the longer ranges in the Mountains.

As stated earlier, this can't be covered with one post.

Good luck and enjoy this rare opportunity you'll treasure the rest of your life.