One of the things you said makes me question the class, and if i were you i would send a quick email to the show secretary to get clarification.
In my experience, i have never seen a WP/stock show have an English class. I have seen mixed shows, like a fair offer line classes that cater to both English and western. In these shows, they would have a stock type horse halter class, and an English type horse halter class. The stock type one was open to those who showed western and the English was open to those who showed English. In the stock type you wore western clothes, jogged, and wore a western halter. And in the English you wore English show clothes, bridle and had a big airy trot.
I own Thoroughbreds and have shown both English and western with them, the below statements are not to be taken as me saying a quarter horse is a better breed then a thoroughbred, just that they were built for different jobs.
I am assuming, from your brief description, the classes offered at your show are only western. One is for stock type horses like the quarter horse. The other is for non-stock types, like your Thoroughbred, who do western. A halter class is judged on the horse’s movement and build. A Thoroughbred who looks like a Thoroughbred will not beat a Quarter Horse at a stock type class. I feel like this class is offered as a way to judge the horses who would not be on the same level as a quarter horse and would have no hope at placing in a class with a bunch of quarter horses.
So that being said, show in western clothes, in a western halter, and band, not braid as you are going to a western pleasure show. Stand your horse up square, and in the way that will make it look best, you will also jog with your horse, not trot. You will need to move with the judge in a halter class, not just a showmanship class if you are stood for inspection.