Today, I trail rode a gaited mare, in a synthetic dressage saddle, wearing blue jeans, suede cowboy work boots, and a cami over a bathing suit top. We gaited, cantered, and jumped. Mare didn't care what I wore and I was comfortable despite this 92* heat.
You're looking for a service, more or less. You are not looking for a fashion guru. Clothes and tack should not matter to the instructor for basic teaching lessons as long as both clothing and tack properly fit and nothing will slip or get hung up. I would only start buying discipline purpose tack if you are looking to go into competition.
Personally, I would take up reining in a dressage saddle in a heart beat. A) I am comfortable. B) It is what I own. C) I think it would be funny.