And now for a different point of view …
First of all — on the type of compass — whatever else you do, get one that settles quickly — that usually means liquid-filled. IMO there is no need for any compass features beyond a basic simple liquid filled compass for back country land navigation.
Next — the original request was about navigating off-trail in the mountains. For that sort of thing, I would strongly suggest good map skills are FAR more important than compass skills. There is no reason that you should need a compass for much other than (perhaps) orienting a map (although you should normally be able to do that visually, without the compass). I would go so far as to say that if the OP has any doubts about his map reading skills, then that is the first thing he needs to fix and he has no business doing much off-trail travel until he does so.
Yes, I can buy the occasional need for a compass, such as whiteout conditions, so I do carry one even though I rarely need it. I can also see one for off-trail navigating through terrain where it is hard to see enough to stay located on your map, but that is rare in the mountains.
All you really need to do is keep track of where you are. Following your progress on a map enough to always know where you are it not that tough — and it's far easier than locating yourself once you have become disoriented (regardless of the type of compass you may have). It's also less time and fuss.
I have always wondered why everyone emphasizes precision with a compass, even though my initial compass work was with a lensatic compass. (We just blew away the other Boy Scouts at compass events at Camporees!)
Over the years I have found well-developed map skills far more valuable. Yes, I understand the neat things you can do with a base plate and with a sighting kind of compass. But in all my years, ranging from Boy Scouts to artillery forward observer out on patrol to extensive backpacking I have found the ability to read a map FAR more important than any compass skills.