It is still the norm to wear a black jacket, white breeches, and white saddle pad in dressage. You could branch out into other dark colored jackets, but I think you get the best range of styles and fits in black as everything comes in black.
Jacket is very personal. If you are well endowed finding something that fits across the chest is job number one. Or if you have long arms, short arms, long or short waist, etc. You might need some alterations. It’s about impossible to take a jacket in at the shoulders or to add room at the chest, but it’s easier to take in the waist or hem the sleeves.
I think most new jackets are in tech fabrics. Some are structured and lined, some are stretchy mesh that look solid from a distance. If you were in a really hot climate those would be a miracle.
I think people mostly have premade fluffy frilly stock tie thingies that have a snap at the back. These are often locally made or on Etsy and can be very pretty. They fill in the throat area of the jacket making it less important what shirt you have on. I read a tip on here recently that if you have a black mesh jacket you can wear a show shirt that has a black body and white cuffs and Dickie. I think that was more hunters. You can wear a short sleeved top under a dressage jacket. But the idea of black top under black mesh jacket is smart if it makes it look that much more soild.
Hair around here anyhow is still some combo of hair net with elastic or clip on bow. You just want it anchored so you don’t end up riding down center line with a giant wisp tickling your nose after warming up for an hour in the blazing sun. Only hunters tuck their hair up under the helmet.
White breeches. Well, first, your jacket should cover your butt :). But you are going to want to give some thought to the pantyline, see through, or ripple effect. You might want to try a Spanx type undergarment or black bike shorts or etc. Again very personal, and if you are svelte much less of an issue.
You can show in your everyday saddle and bridle. I don’t love the rhinestone look but a brownband is easily swapped out, just do a trial run to make sure it doesn’t fit weird, the wrong brownband can make a bridle too tight.
You can also show in your everyday helmet. And tall boots, shined up. And your regular black riding gloves at lower level.
So really you need black or dark jacket, white breeches, a cute premade stock tie, and several spotless white saddle pads that can be washed in hot water with bleach after the show and stored somewhere safe.
I’m just always a little superstitious about getting too much gear for a new endeavour, so my recommendation would be to just get the basics for the first year and not try to visually stand out.