I wouldn’t bother with combinations of bones, drivers and shapekeys. I agree with @davidrodriguez. You can do it with bendy bones alone (and solid skinning ofc) followed by a little bit of corrective smooth.
I dont even bother creating whole face cages anymore (as in the picture posted by 3dioot). I used to but i hated it. Who likes to skin 200 facial bones right? Check out my WIP thread.
As for the meatball and minion characters as well, they used something like a face plane, following the overall shape of the face (or body in case of minions) and constraint the facial bones to it. Take a look at shrinkwrap for bones.