A "classic" is typically going to be the one that we got as a boy and grew up with before moving on to other options. And now we're all teary eyed with nostalgia over the "Classics".
So the grey and no hair folks among us I'd say that for Canada the more common option is likely some form of single shot Cooey. In the US it would likely be Gramp's old Stevens Favorite, Crackshot or similar single shot as made by so many companies. And if Gramp's boy's rifle was given to some other youth in the family then likely as not the others ended up with Dad buying them some brand of pump action or single shot bolt action.
On the other hand for the younger generation the Ruger 10/22 has been in production for a LOT of years now. So anyone in their 30's or less is likely going to see that as their Icon of Nostalgia. Never mind that it's still as popular a rifle as ever.