I would definitely wear white under the jacket, that's for sure. As for what it is, the stock tie will cover most of it up. I wouldn't wear like a tshirt, it needs to have a collar. Dover Saddlery | Romfh CoolMax Short Sleeve Dressage Show Shirt .
This is the shirt I wear under my show coat. It's not like a normal show shirt you would see in hunters, but it has a collar, and is actually for dressage. If jackets are excused, I just wear the same shirt tucked in with a belt. It looks alot better than a polo.