for me, when traveling or moving non-combat I use the mouse, the side button is a run as well as holding two buttons down at the same time. I do my best to move like this.
as for combat, I try to move my team as little as possible and use my tank to pull to the team.
if the team isn't following the tank around then I use the keyboard and they all move at the same time.
this is a kind of limited move such as a small move to get out of aoe area. this frees up my right hand to push buttons on the keypad or use the arrow keys to run the team left/right.

I have special keys on the keypad that I have mapped to function, like keypad-7 & 8 are for totem drops keypad-9 is water shield and keypad-1 & 2 are for healing a main tank or an off tank.
The only time I kick-to-play is solo boxing a healer in a large raid, here I use healbot and left or center click people on the healbot buttons.