If you make any kind of activity or extreme outdoor sports, or even traditional, but particularly “active”, most likely have to have the camera always on hand and ready to fire with a good scene. In that case, the risk of bumping due to falls (cycling, riding, skiing, etc.) Against a wall or rocks (in mountaineering, rock climbing, hiking, etc..) Will be quite high.
A sheath for carrying the camera will be essential. This case must be tailored to the activity to be undertaken. As an example, if you are dedicated to climbing, you can not use a holster that does not have a strap to hang over the shoulder, but a simple handle to carry by hand, something completely useless.
The cover must be waterproof, or at least distasteful or “repellent” to the water to some extent (remember that we will be outdoors, weather and demand), and also be cushioned to some extent, to protect the occasional camera shots. Should be easily accessible, with zippers, and compartments also thank designed to save battery and memory card you want to have on hand as a replacement. A hanging strap to the neck or shoulder can be very useful also in outdoor activities.
As a precaution, it should be taken into the camera case, one or more bags with “pills” designed to absorb moisture, and usually come in the packaging of electronic products (just) to avoid damage to components condensation due to high humidity.