LOL... this was best overview of Quaternions vs Eulers ever. I still don't understand how Quats work, but all I know is DEFINITELY avoid on the root bone if you're making game animations with root motion. Trying to make a barrel-roll or similar animation is so much easier when you have degrees... :-)
Don't give up on quaternions. You will get the hang of them, remember it's the fear they sense.
Always use Euler for 1 or 2 axis of rotations. But if you need 3 axes not being afraid of quaternions will get you to the end goal with less headaches.
A barrel roll in Euler will not be easy depending on the rotation order and the starting direction.
I personally use Euler on the IK hands and feet and root, but I'm prepared to switch to quaterion if/when I run into trouble.
You will find your own personal preference too.
Hope that makes sense.
(Other programs don't let you switch between Euler and Quaterions at all - thank you Blender)Thank you, Wayne! That's cool that Blender is so flexible in that way... :-)