Trailblazer: Do you know anything about barrel racing? I have no clue why you're bashing NY. First off, if horses aren't started on barrels by the time they're about seven they'll probably never go anywhere. Second, horses should usually be retired from barrels by 18 because it's very hard on their legs and minds. Very few ponies will make good barrel horses, and even fewer Arabians. News flash: Not any horse can make a barrel horse. There are hundreds of factors, among them breeding, conformation, intelligence, heart, mind, and soundness.
I don't have a horse for you, NY, but you'll be lucky if you can get any sort of barrel horse for $1000. Even a 3D horse will run you about $3500. A 1D horse will be anywhere from $8000 to $50,000, and I would avoid Arabs, if I were you. If you're just going on a local circuit, just buy any suitable horse and pay someone to train it for you.