How to work on a horse for western show?

By the way you worded your question, I am going to assume that you have never been formally taught to work with gaming horses. Gaming is not all about speed, it's more so about being able to perform the patterns flawlessly. You need a horse that can turn with ease, remain under control before, during and after the run, and listen to your hand, leg, seat, and voice cues. You also need to be a knowledgeable rider and be aware that yanking a horse around turns and racing around an area is not good gaming. If I had to choose a horse out of the ones listed, I would say either of the QH's, but both sound like they need work. The first would need to learn how to turn, and the second would need show exposure as well as turns. The other two just sound like you're asking for trouble; a large thoroughbred with lots of go go go and absolutely no whoa is a horrible gaming choice. And the thought of throwing a horse immediately after being saddle broke into gaming is a bad choice as well. I know you were probably hoping for a nicer answer, but I just want more people to think before they game. Be smart, get a trainer to help you, and good luck.