The choice of calibre is highly dependent on the game animal being pursued and is influenced by a variety of factors, which would include, without being exhaustive, the nature of the federal and provincial hunting regulations because they put limits on the calibres that can be used. It would also depend on the personal choices and preferences of the individual who is out hunting. The hunter will generally select a calibre, and a firearm that uses that calibre, that the hunter believes will be humane and effective for the particular kind of game they are pursuing.
To circle back to your question and what calibres are appropriate or which calibres are commonly used, that will vary highly depending on the kind of game animal. If a hunter is hunting ducks and geese, for example, they're obliged by regulation to use a shotgun with a certain range of gauges. In the case of hunting big game animals, the hunting regulations, which are under provincial control and do vary a little bit from one province to the next, will generally put limits on the kind of cartridge that can be used for hunting certain game animals. To give an example, wildlife regulations would not permit the use of a rimfire cartridge for hunting big game.