Personally, I was brought up by a Brazilian GP trainer who specialized in show jumping and his own brand of equitation, so I was trained slowly and steadily one area at a time. Seat first, then leg, bridle last. Rhythm, control, anticipation, and feel were the main focus. Not so much looking fancy or getting the horse to do anything special, just a big concentration on my feel and awareness of the horse's body and mine. So, I ride with my seat first and then my leg, last my hands. The horse I was most often paired with is now my own horse, and she's sensitive to the aids, so if I ever did hang on her in any way she'd let me know! I like to keep a classical seat, in the beginning years I didn't really pay attention to the technical terms and just did whatever my trainer set me up for and told me to do, so when I think back I can remember doing a jumper seat sometimes and a classic seat others. It was all about making sure I knew what "right" felt like. Nowadays, it's been a long while since I had a trainer at his level, so everything I do is by myself with a little help of the camera and some friends that generally know about riding. The horse is the best trainer when you know how to listen ;) So, I like to ride with my lower calf muscles extended so that my leg is long and my heels are level, and keep my heels off the horse. The lowest part of my calf doesn't touch her. The largest part of my calf does. It's more like my muscles are working to stay still and extended, not gripping. I like to ride in shorts sometimes when my horse's hair is longer, and focus on keeping my lower leg just close enough to feel her hair tickle me, and not touch her skin. Toes forward, level. When I want her butt engaged, I put the entire leg on with a little or no heel. When I want a gait picked up or a higher speed, I add heel or pluck her sides with my heels. For lateral, I put weight into one stirrup or put my heel on her side.
THIS is a great video for the classical seat and how to fix problems, it really helped me when I got a chair seat and pinched knee when my horse's arthritis first showed up: