You need a well ballenced horse when you search for your barrel prospect, you can start off with the hooves, make sure they're well ballenced, move to the pastern, shoudln't be too long or too short, move up to the legs, should be straight not over at the knee or back at the knee, (btw this is just a really quick checklist) The neck should be sleek and long to balence the body, because the balence of the horse should be about the middle of his rib cage, if his neck is too short, he is able to stop his momentum quickly, and he wouldn't have a long stride, The shoulders should be nice and wide, long and sloaping, and a good with between the legs for room for his lungs. The nice sloaping scapula gives your horse a nice long stride, a short steep angle on the scapula, gives you short strides, Your horses head should be straight, too much of a dish or roman nose restricts airflow, and affects your horses bodly performance, your hind quarters is your powerhouse, your get up and go, your umph! They should match the shoulder in angle and length, you want a short canon bone in the back legs and the frong legs, the croup should be long and sloaped slightly. Your withers shoudl be placed as far back in the back as it can, this helps your length in stride, horses should have a long underline which is the distance between the stifle and the stifle. Horses should have a good depth in ribs, where as the lungs are housed ribs should also be springy. Nostrils nice and big, and that should cover your bases!! Hope this helped!
you can start with nothing, and out of nothing or no way, a way will be provided.