Generally in lower level dressage you can wear white or beige/cream jodphurs/breeches. Even at the lowest levels black is not a suitable colour for jodhpurs/breeches. Most people wish they could ride in black - its a lot more flattering - but that is not what is done. I am not sure exactly why these colours are used, probably a mix of tradition, smart looking and make the leg position visible against the saddle which can be important in judging.
Bands rarely look good in manes, and if you use them you must use a colour that suits the mane. Black or white is not a good look in chestnut main. Choose browny bands, or even clear ones if you are desperate. Sewing braids takes little more time, but they stay in securely and look much better.
Colour is not used in the dressage ring. Dressage is one of the oldest sports in horse riding. The riders generally take it very seriously and if you were to use bright colours it would probably seem disrespectful. You are best to use a white saddle cloth or numnah, and black or brown leather tack.
Unless you are at low levels (pony club type deal) you will be expected to wear either long boots or gaiters. I have a pair of Ariats - I call them chaps but they are generally considered gaiters. I don't know what the actual official difference is, but if they have smooth shiny leather on the outside generally they pass. Ensure your boots and gaiters are the same colour.
As far as I am aware show and dressage jackets are different, but again at low levels either should be fine. Black or navy.
Be aware generally you are not allowed to have bandages or boots on the horses legs. In the few unofficial shows I have been in they do not allow whips or aids such as martingales. Bits and spurs are often limited to level.