When just looking at a random dog that may or may not be purebred, my first glance generally takes in broad strokes - coat type, rough body shape, head - because I want to see if it's a breed I can identify. My wife and I have kind of an ongoing game to see who can identify random purebred dogs we see out (there's more purebred dogs than mixed breeds in Norway) so I'm often more interested in IDing the breed in general than evaluating conformation. My best win is when I somehow recognized a Danish-Swedish Farmdog on the fly, still not sure how I managed (they're more common here than in the US, but still pretty darn rare, and they look very terrier-y, even if they're technically in a different group). Because of this, sometimes I'll be looking for unusual traits like double dewclaws if I'm trying to confirm a breed ID.
But I'd say that in casual encounters, my eye does tend to go to the face and expression first, though as a poodle owner I also am very quick to notice movement in poodles and poodle mixes too. I don't know much about conformation outside of the breeds I own (and even those I'm far from an expert), so if I'm critically evaluating a dog for some reason, I'll be looking at obvious things like topline, knees (basically does the dog have them or not) and musculature. For curly coated breeds I may look at coat texture, and for brachy breeds I'd pay more attention to how extreme the nose is in both length and nare size/shape, but like I said, I don't know enough to pick out much outside of really obviously poor conformation.