Survival and SAR experts strongly recommend staying with the aircraft or vehicle in most circumstances. Even if on foot, it is generally a good policy to simply stay put and let SAR find you, unless there is little chance they will come looking because you failed to notify anyone before leaving. In any case, a compass is a necessity if you should have to travel, for whatever reason. In many areas it is the only reliable way to maintain a straight track through the wilderness. Select a quality compass that is easy to use.
For years Silva, from Sweden, was the best known manufacturer, at least here in the U.S, followed by Brunton and Suunto. In recent years a number of other brands have come to the market, including Recta (Swiss) and the industry has seen considerable consolidation and you'll notice many of the compasses with different brand names are identical. Recta is now a subsidiary of Suunto.
The good news is that for the average user, it probably doesn't make a bit of difference. All have similar product lines and make generally high quality equipment. It's the small features that differentiate among them. Whether those features are important for your uses depends in large part on your capabilities in using them.
Small pocket compasses, mini-compasses or button compasses can fit into a pocket, into a personal size survival kit, or worn on clothing. Every manufacturer offers versions in various sizes including some designed to fit on a watch band, to function as a zipper pull or to be pinned to your clothing. Any button compass selected should incorporate some means of securing it. Otherwise, once out of the kit, the minute compass is easily lost. Most button compasses have a groove around the circumference that is normally used to hold them in a larger device. For our purposes it works great for holding a short length of non-magnetic wire (brass or stainless), twisted tight with a small loop added by which it can be attached securely to your person with a lanyard or similar device.