Don't focus on the breed so much as the individual horse. Many Quarter Horses are good, calm Western horses, as are Paints, though Appys are known to have a bit of an attitude. Of course, this is a generalization, and there are many great beginner horses in every breed. Look for a well-broke schoolmaster to learn on. Good luck!
I've seen plenty of thoroughbreds that were just as good as quarter horses at western sports. And my quarter horse/ arabian beat the quarter horses every time he entered the competitions- he's a fast little guy! I really like crosses, and for western sports, quarter horse crosses- appendixes, quarabs. I'd look into those also. BUT. Most of all, keep in mind that it's the individual horse that counts, and how well you work with them- not just the breed! Good luck! :)