I dont know much about barrel racing, but as with any other disicpline, look for a horse that you can actually click with. Ive seen people pay years worth of saved up money on that "perfect looking" horse only to be disappointed in the end. Of course you dont want confo issues that will become medical issues, but a small head and big ears never killed anyone. If you know people in the barrel racing circuit ask around and listen to their opinions. Or watch a few rodeos and see which blood lines, body build etc, on average, perform the best. And, as im sure you know, ALWAYS take your potential buy out for a test ride. :) Good Luck!
A Dog looks up to a man,
A cat looks down on a man,
But a patient horse looks a man in the eye and sees him as an equal