Carp are tricky in that there is no "right" fly for all carp, but there probably is a "right" fly for your carp. Rule number one is to know your forage. Figure out exactly what the carp you are going to chase eat as their primary forage and then tie a fly designed to look and act accordingly. I have caught carp in a bunch of states now, and it is pretty amazing how different their forage can be. In ID we fished for them in a resevoir full of leeches and caught home on mohair leeches. On lake MI they chase and eat lots of gobies, so we catch them on big 2 inch long sculpin patterns. In my home water of the Columbia they eat mostly clams or nymphs, so out here I catch most of my fish on a hybrid.
Carp can eat just about anything, but if you figure out their primary forage it can be a big help. Took me forever to figure out they were eating clams out here...once I got that down it not only helped with the fly selection, but with how I fish it. Clams don't run, so I barely move the fly on my home water.