In the short amount of time I've been barrel racing, I've rode nothing but Quarter Horses. I don't have anything against other breeds, I just like keeping it simple with a breed that I know can excel in barrel racing (given that they are actually bred with performance lines and have the want to run). My mare is 14.3hh, but basically all leg. She has a lot of racing Quarters and TBs on one side of her pedigree, and on the other side you will find nothing but cutting and reining horses. I think this combination makes for a darn good horse.
I actually prefer taller horses for barrels, but I also pole bend, and I have a lot of trouble getting big horses through the poles.
Red Money Maker (Red) - 2004 Sorrel QH Gelding