A good helmet, breeches, tall boots, and a SAFETY VEST [a must for cross-country.] There's the normal english show attire- coat, gloves, black helmet [preferably], shirt, tan breeches, black boots [all for Dressage and Stadium.] For XC, you MUST have a vest. No show clothes there, but tall boots and breeches, helmet, gloves... shirt is up to you what color/ style you wear. Most often it's either a t-shirt, polo, or long sleeve.
In both stadium and cross-country, your safety medical armband is a must.
For your horse, on the XC, boots are also a must. NO OPEN FRONTS. They could allow your horse to bruise his legs. Stadium, same thing, boots are recommended. For jumping, a breastplate is often seen; it's a preference/need thing. My saddle doesn't normally slide, but if I'm galloping and it happens to, I'd rather have a breastplate on for extra stability. No martingales. That's all I can think of for now; I'm sure people will be able to add onto this. =]
OH! If I were you, I'd check to make sure you can gallop in a plain snaffle- I know my horse can on XC, but it's not the same fat snaffle I use in dressage. Safety first. =]
Also- rubber reins for jumping: I prefer them, esp. When you're riding thru water mid-course and don't want slick reins the rest of the way through the course!