To expand on what equiniphile said; for the lower levels, light tan or beige breeches are fine for dressage. In fact, I'd recommend them, because you can use the same one for show jumping and XC provided they don't get too dirty on day 1. My advice is to just buy a pair of your favorite brand of breeches in a light beige or tan color and keep them only for shows. You will need gloves for dressage, but I suggest black, unless you have very, very quiet hands. White gloves make it easier for the judge to see your hands, and if your hands are still a little busy, you don't want the judge to see that!
When you look at vests I suggest making sure they're certified. Tipperary vests are very popular due to their comfort, but they are NOT safety certified! Look at Airowear, Woof, or Charles Owen vests instead. If you can swing it, look into getting a separate helmet for cross country as well. A Charles Owen skull cap would be a great choice. For dressage and show jumping I have a Charles Owen JR-8, but many others have a GPA or something similar. You will need a medical armband for both jumping phases.
For your horse, riding in a jump saddle for the dressage phases is fine at the lower levels, if a little uncomfortable (in my opinion), however when/if you get to preliminary level I suggest looking into getting a dressage saddle. For pads, you'll want conservative colors. I use white for dressage and show jumping and a dark, hunter green for cross country. No boots or polos are allowed on the horse for dressage, but for cross country try to find some good quality boots that will protect the leg well as well as some bell boots. I really dislike strictly neoprene and prefer something with a harder plastic or carbon fiber shell. I've had a horse sustain a NASTY puncture wound on cross country because it was only wearing neoprene boots. For show jumping I suggest some open-fronts or just go bootless for the lower levels unless you horse has an issue with over reaching.
If you don't have breastplates, you'd likely want those as well for the jumping phases.
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