First Thing's First
If the horse doesn't have a good feet, you're fighting a losing battle. Start at the feet and make sure the feet are good enough that you'll have a horse left at the end of the training process. You want a good foot and a good heel above all else. I've made that mistake too many times.
If you're looking for a head horse, the horse needs to have a back your saddle will fit and not roll around. It needs to have some withers—not tall withers, per se, but at least some. He'll get sour if your saddle is always rolling and if you're always pulling on your saddle to get it right.
I prefer one to be 15 hands to 15.2. Sometimes I get them bigger if they were racehorses, but that's my preference.
[Related: Size Matters: Insights on Head Horse Size]
I don't like the neck to come out the top of the withers. I like it to come out lower so it's level. That keeps a horse running flatter.
Obviously, I want a big hip and a long shoulder. I also like them to cinch deep, because that's a good sign they'll be strong and able to run, too.
Top and Bottom Lines
I look for a shorter back and longer underneath—that's another indication he'll be able to run. That will correlate with the length of his stride.
[Related: The Search for Prospect Roping Horses]
Obviously, straight legs, shorter cannon bones, and hocks closer to the ground are important. That will all help a horse be durable, stop and take a pull on his hind end.
The mind or willingness can't be overlooked. I've had horses with all kinds of tools, who were athletic and capable, but not willing. They made me work for every ounce I had.