Best Exorcist would go to either Kagome(iny Yasha) or Yakumo Fujii(3X3Eyes). the reason i say Yakumo is because that is what he does for the 4 years he is seperated from Pai. and he is good enough at it to gain notoriety throughout the demon world.
I agree, Yakumo would gain a good reputation. He knows martial arts, aswell. Also, he cannot die (in a way, you know what I mean if you've seen it).
But, I believe Kagome has delt with stronger demons, so I feel it should go to her. 3X3 Eyes was more of a love story, in a way (not saying Inu Yasha isn't, but Inu Yasha is more recognizable, longer, more in depth, etc etc).
Good choice with Yakumo though, I almost forgot him.