Personal opinion, for what it's worth. A restoration project should only occur if there is the prospect of returning a gun to as near an original condition as possible, with all parts showing the same degree of 'wear'. This might require the making of missing or damaged parts, and refinishing techniques for metal and wood using techniques, materials and tools as close to the original as possible - no shortcuts. This can be costly and time-consuming, with uncertain results. Frankly, very few guns that have been used and abused to the degree of your piece would merit such work, outside historically important pieces, and access to a museum-grade restoration lab and skilled technicians would be required. Anything else would result in a worthless pile of overly cleaned brass, rust pits, and sanded wood. A very mild clean, with mild detergent and a toothbrush, might remove surface grime without affecting the patina, but I would nevertheless be careful about doing so. I would also caution about using a screwdriver anywhere near the gun, damage would be almost certain.
That was the bad news. What you have is a wonderful piece of Canadian history, with origins in Industrial revolution Birmingham. When I suggest it shouldn't be restored, I do not mean it shouldn't be treasured and appreciated. Build a nice wall frame for it, and display it with pride.
And with the money and time you've saved by not doing a DIY restoration, may I suggest acquiring some good books on the subject of trade guns and their production. I can recommend Empire of Guns: The Violent Making of the Industrial Revolution, by Priya Satiya. This gives the setting and history of the Birmingham gun trade in the 1700s that produced the gun. An excellent book. And a quick Google search on trade guns brings up a number of titles that might shed light on your particular piece.
Enjoy your very good find!