Well, for hunters, it's all about looking conservative, tidy, and traditional. You'll need a hunt coat, usually navy blue or black, beige or white breeches, tall boots (either dress or field boots), and a button-up shirt with a collar to go under the coat. You'll also need black gloves and a show helmet, but you can get velvet helmet covers which are a lot cheaper. I think show jumping is similar. You can find all this stuff at the stateline tack website and on tackwholesale.com.
Legacy Tack has a website that has some good prices, too.
Another option that I see at the small shows that I go to is a dickie in lieu of a show shirt, over a tank or tee and under the jacket. Much cooler in the dog days of summer, more affordable (you can even make your own without much trouble), and I can't tell the difference in the ring. A bigger show, go with a full shirt.