Wax first, then polishing compound to remove the wax? Hmm.
I’ve used the product below on several different vehicles for removing light surface scratches, it works great. Use a microfiber towel to apply, rub in a bit then wipe it all off and check the surface. I’ve never cut too deep on dozens of applications, but if you lack experience it’s far better to go slow.
Meguiar's Scratch X has worked pretty well for me to remove light scratches. I also like to use Poorboy's World Black Hole glaze topped with wax or sealant to reduced the appearance of paint imperfections.
Without using a DA buffer, try getting chemical guys v36 and v38 (you can get both as a set on amazon small bottles for like $25). Wash then Clay bar the car. Then using a microfiber applicator pad, rub in the compound in small circles to the areas, starting with v36 finishing over with v38. Then polish and then wax the car.
Most scratches are superficial and come out with a light compound. I've seen a lot ofpeople, including myself, use too heavy of a compound and make the problem worse. Anything advertised as a complete compound is usually a medium finish, which still needs to be polished in.
I'm a bit of a strange guy and I own way too many polishes. I've started paint correcting my friends cars for practice and I charge them buffers or pads or compounds etc lol