Yes, for schooling shows half chaps and paddock boots are fine. Granted, you would probably want them to match (No brown boots and black chaps, or vice versa) but even then, depending on the show ...
Breeches: Beige or greenish beige for hunters would be acceptable. And in the summer most schooling shows will waive off the jackets (especially in the south) and you can wear just a normal show shirt, or in some cases, a nice polo shirt. (The color of the show shirt varies by person. From plain white to pinstriped, soft pastels, etc. Polos can be just about anything, but I might not go for magenta.
If you do decide to get a jacket, dark blue or black would be fine.