I can't see why you MUST know anything about English dressage in order to learn Doma Classica except for the fact that the two systems have much in common - after all the horse in both systems has four legs and the rider has two. If you did know something of English dressage, then it would be of help to you.
If someone started up locally to me a school in Doma Classica, then I'd go along to see for myself what the differences actually are. But I'd want to find at the school an Andalucian horse, a traditional Spanish saddle and a male instructor wearing a bull fighter's hat who spoke English with a Spanish accent. Actually I'd probably be more interested in Doma Vaquera (the countryside style) which I am told is how a young Clint Eastwood used to ride before he reached pensionable age.
As an afterthought, I think I would prefer to find a riding centre located near Jerez in Andalucia where the sun is warm, the sea is blue, the beaches sandy, the food tasty, the wine cheap, the horses are absolutely stunning and the ladies are very beautiful. I'd probably never go home.
Be advised, that if the centre you are going to use is typical, you'll be learning on stallions, so what you'll need are light hands, a firm seat and an upright posture.