I do both at the same time.
Start with the hair and face and then down on the outside, down the legs and then groin.
Always end with the feet though as I want to put socks on right away.
I usually put my socks on in the order of how I found them.
If I find the right sock first (or it is the outer one if they are "folded" into a sock-roll-thingy) I don't wait and take the left on first.