It sounds like you're set.
For the saddle, you should have a clean, white square pad (for schooling shows other colors are acceptable as well, but make sure it's clean and in good repair). If you normally use a half pad for saddle fit, use it as well.
I assume when you say you have a "regular" English bridle you mean it's a plain snaffle bridle (no flash or crank cavesson), and it's probably brown instead of black (I found out when shopping for a black one just how hard it is to find a plain snaffle bridle in black!) This is fine for schooling and local shows. If you get to riding higher levels at rated shows you might consider getting a bridle that matches your saddle (which I'm assuming is black) but you never need one with anything other than a plain cavesson unless you get high enough level that you're considering a double bridle.
Breeches in a conservative color will be fine along with a tucked in polo shirt and a belt. Paddock boots with smooth leather half chaps of the same color are allowed up to 2nd level, so would of course also be fine for a schooling show. Suede half chaps would be OK for the schooling show, but would need to be replaced for recognized shows.
Braiding is never required at any level of dressage, but is customary. Most people pull and do button braids, but there's no style of braid required or even mentioned in the rule book. I put my horse's mane into a running braid (it's way too long to do button braids and I'd sooner stop competing than cut it short enough for button braids) I'd recommend braiding the forelock into a small button if you can; it looks a lot cleaner than leaving it down.
“The horse is a mirror to your soul. Sometimes you might not like what you see. Sometimes you will.” - Buck Brannaman
"Nothing forced can ever be beautiful." - Xenophon