If you want to show, and are new to horses and to the showing environment, you would probably find it less overwhelming if you had a coach to guide you through the process. Are you in riding lessons currently? If so, ask your coach about what there is locally.
There are indeed very basic beginner type classes that are walk/trot. These might have beginner riders in them, but they might also have experienced riders with young horses that need the exposure to the show atmosphere.
The 3 basic divisions in English competition would be dressage, hunter/jumper, and rail or “hack” classes (where you have a group of people in the ring doing different gaits to the judge’s commands. In dressage and hunter/jumper rounds you are alone in the arena.
At schooling shows, there may be walk/trot classes in all these divisions, and the hunter/jumper classes might have a poles class where you just trot over poles on the ground. These classes might be primarily for small children, though.
As far as doing a walk/trot dressage test, despite it being very basic and no canter, there are still a number of things you need to do such as have the horse moving appropriately, and be very accurate with riding your pattern and your transitions. And even for a trot poles class, you need to be able to remember the pattern and keep the horse moving smoothly. Some coaching would help here.
I would recommend first going and watching a show similar to one you would like to attend, and pay particular attention to the classes you would like to compete in.
I would also give some thought to how your horse behaves off property. Shows are high energy environments for horses, and even the kindest horse can get worked up and frisky. Also you will need to ride in the warm up arena which at a schooling show may be full of other frisky horses, including green OTTB ridden by trainers, and tiny ponies whipping around ridden by tiny children. How do you feel about navigating chaos?
Also, when you say your canter is a work in progress, what exactly do you mean? If your horse got frisky and decided the canter in a walk/trot class, or in warmup, what would happen? Could you calmly and effectively bring him back to a trot, or would you get unbalanced, tilt forward, panic, fall off?
It’s fine to bring a horse to a show with the intention of only participating in the walk/trot classes, but I think it is dangerous to bring a horse to a show if you are not comfortable riding him and controlling him if he decides to canter.