My main input would be to look for one that is has a durable bottom to not deform or mar the reel when you sit in on rocks or when you are climbing over things. Also; maybe look at a light-reel that does not have the large diameter of the average fly reel as you usually do not need as much line.
Another big issue is will it balance the rod you plan to use it on? You should select a reel with a weight that you can easily manipulate the handle with easy and balance.
That being said; I rarely fish the mountains and know very little about what reel is the best or not.
The things I mentioned are the points I would consider.