Should I use Matinee for this?

I have a pachinko-like physics demonstration, and I’d like to create some kind of guided camera that follows the movement of the balls. I have never used matinee (or any custom camera rig outside of the template player cameras), so I’m not sure how I should approach this. I’d like to be able to adjust the vertical, front/back, up/down movement as well as tilt.

Here is what it looks like with me just using the mouse to tilt.

48 Second Clip

In my mind, I’m imagining creating a custom timeline that animates a camera doing all of it’s positional and rotational changes, and then I would drive that timeline by finding the average Z position of all the balls in the scene, where the starting Z position of the balls represents the beginning of the timeline and their resting position at the bottom represents the end.

Am I on the right track, or is there a better way?