For me, it depends on the gender. For women, I tend to take-in the entirety of their face, because I am really fascinated by the variety of faces women present to the world though their makeup. Once I take that in, I suppose I center on eyes, as that seems to be the area that receives the greatest amount of attention, makeup-wise, and seems to convey a lot about themselves.
For men, I think I tend to check their hands first. I think that's because, when meeting another man, it's pretty much a given we will shake hands, and I get squicked-out by unkempt hands and especially nails. Long nails on a man are especially unnerving to me. One doesn't have to go to a salon to keep your nails neat and tidy. And, there's also the matter of the size of their hands. I'm not blessed with big, burly man-sized mitts, so, if he has big hands, I know I'll have to adjust my grip a bit.