I hold it both ways.
Basically when my hand is father away from the mouse I use my fingers(If I'm reaching for the mouse, then its just the front part of the hand) then I rest my whole hand on it. I don't move my whole hand to just move the mouse, I just use a flick of the wrist. That or I move the mouse under my hand with my fingers(I have high sides on the mouse so I use my little finger and thumb to move it back and fourth.
I think using your fingers with your whole hand or most of the hand on the mouse pad extremely weird though. So to me, you people are weird.