Auger sizes really depend on how you're setting posts. I, because I'm crazy, hand tamped mine (about 100 of them); I can assure you that these are set as good, if not better, than driven in- I alternated materials (some excellent stuff that packed liked cement)- and at 3 1/2' deep for 4 1/2' out of the ground they're insanely solid (some were put in places where water existed a mere 2' down!
I rented a skid steer with auger. Wanting to say that it was a 12' auger (a good 2x post size- if one is going to tamp; also keep in mind that your string line, or whatever you use, isn't going to be perfect, so having a little bigger hole allows you to correct for that). All said, what I found doing all this was just how incredibly heavy all the material collecting on the bit can become. I've got some pretty heavy clay. The skid steer is one hole-making machine, and I had several holes that the skid steer struggled getting the bit out of the hole (I was burying past the head). I could ask my rental guy who makes that attachment. I know that he only buys the best. Oh yeah, I dug about 100 3 1/2' deep holes in two days (using different spotters, so had allowances for "training").