Feel free to PM me if you have any specific questions. There's a LOT to cover, and I don't want to overload you with information all at once :)
Here's a go-to manual for judging: http://www.usef.org/documents/ruleBook/2012/16-HU.pdf
A hunter should look easily-guided, with an even, flowing stride and an alert but calm expression. The horse should look interested in the jumps, not resentful or anxious. In a hunter class the horse's form is being judged, while the rider's form is judged in an equitation class. Here's a few hunter rounds to give you an idea of what a hunter should look like:
For a local schooling show, your horse does not have to be braided. Usually riders have numnahs/shaped white saddle pads, but I have seen just half pads on occasion. Close contact saddles (squared cantle as you move up the levels, but for local shows it doesn't matter) are preferred, but locally you can use an all-purpose. Properly-adjusted standing martingales are permitted, but no running martingales. Simple cavessons; no drop/flash/grackle nosebands.
For yourself, you need a ratcatcher with a collar, a neutral-colored show coat, tan/beige breeches, black field boots, black gloves, and a belt. Your hair should be out of the way. Some people can stuff it into a net and flip it up under their helmets, but if you have longer hair, a tidy bun (with a cover, if possible) will suffice.
I haven't even scratched the surface of hunters. Hopefully some of the more knowledgeable hunter riders will chime in :)