In my opinion if you are going to choose any kind of firearm for long term wilderness survival, then it should be the flintlock. Even after the percussion lock was invented in the 19th century, those who lived and worked in wilderness areas preferred to keep their flintlock.
You can always find a piece of rock that will work in a flint lock. The whole gun is just lock, stock and barrel. If you carry spare parts they are easy to replace if something should break, and if you have no spare lock parts you can still use the gun as a matchlock.
A .32 cal rifle will easily take any game that a .22 will, and it will do it with only 14 grains of black powder.
A fusil will digest bird shot, swan shot (buckshot) and round ball and will take any game from birds to buffalo. You can also use a combination of any two shot options, such as swan shot and round ball, or bird shot and round ball.
You can adjust the amount of gunpowder you use for each individual shot, and you can retrieve your lead from the game and easily remould it for further use. The lock can also be used for making fire which is a good back-up.
A fusil lock with the hammer forward and the pan open. The cock is on half-cock safety.
A .62 cal fusil. Note the hammer stall/cap tied to the trigger guard. This is an extra safety precaution.
A .32 cal flint mountain rifle.