I honestly don't know much about barrel bloodlines...what wins and what doesn't, but some customers of mine breed horses that they use for feedlot work, barrel racing, and team roping. Most of their broodmares are by a stud named Perfection John (most of them a couple generations down as PJ was in the early 70's) and they are using a Rocket Folks stud. If I was looking for a good barrel horse, I would probably look to buy one of theirs. What they breed has very good conformation, incredible athletic ability, and really good minds once you get them started (the starting can be a...ahem...challenge).
I don't claim to be a barrel racer but, I rode a Captain Biankus bred mare that was a lot of fun! She was super light and sensitive and she got really low in the front going around the barrels. Which I guess is the norm for the Captain Biankus bred horses. She was a 1D horse and ran in the big shows....it was like riding a cutter around barrels.
I like cutting/working/cow on one side, racing on the other. That way, you get the speed, but you also get that natural "rate". They seem to hunt the barrel down. :) Names don't matter to me. Great racing champions many times were complete flukes, sure they had good bloodlines, but they don't make a horse. Heart and want to work do.
I don't care much for names either. Cutting on one side, racing on the other. The only stud I really liked was Dash Ta Fame because he was just WOW, and was actually going to breed to him but a few weeks after I decided I was going to he passed away... How awesome right? LOL.