You can jump pretty much any horse or pony, especially if you are a beginner. The important thing is that it is healthy and on the young side, so it won't have arthritis. I think a Quarter Horse is a good breed to start with. They are versatile and have great temperaments.
If you're just learning, you want one that's been there and done that so it can teach you what you need to know and allow for your mistakes. As for breeds, there is no one breed for it, it's all about individual horses. I've seen great thoroughbreds and ones that couldn't get out of their own way. So, generally speaking... Most people look at Tbs or appendix quarter horses, warm bloods, etc The body type is usually leaner and leggier, you would want to avoid foundation bred quarter horses.