It depends. When straight, the horse will first start with his hind (if the back is carrying correct), when asking a slight turn around the forehand circle, you must ask the shoulders to start first, or else the horse will fall on to them and the exercise is lost. When turn around the quarters, you must ask the hind to start but only allow movement from the shoulders sideways and so forth.
So it all depends. The whole point is, to make sure a horse will stay healthy under a rider, he must be able to use forehand and hind quarters independly from each other. But that will all come later, now you want your horse to start moving from the hind, as that means he is using his nuchal ligament and his longissimus dorsi is free to produce correct movement right from the start.
So, when you want to go forward, lean slightly (!) back and open the front of your body, when wanting to halt, lean slightly to the front, when wanting to go backwards, lean a little more to the front and take your legs back a little.
It is not my invention, nor of any master, it is the natural reaction of any horse who has the choice of reacting. They all react as such I have witnessed for over 20 years.
Concerning Parelli, I can not tell you anything, I have never seen anything from it that made me want to study it... sorry...