100% agree with Paul.
Another thing that most people mess up on is the relaxed part. It's not relaxed like a wet noodle, it's relaxed with dynamic tension. Your upper body should feel like it is resting into your lower body, your lower body into your feet, your feet into the ground... Use your bones to support you, which requires excellent posture and balance.
Once you can stand still in relaxed but dynamic fashion then you can start to move properly. When moving let the body guide your attacks (yes I am of the formless school) if you stay in balance with a full center and everything driven from the feet you will find that you are much faster and more powerful.
Keep in mind that the shoulder is not part of the punch. The punch starts from the feet, to the center, to the elbow. Another way to say it, the the foot moves the hip, the shoulder moves with the hip, the hip drives the elbow, your foot and fist land at the same time. Make sure that when you punch you are not twisting your body and that your shoulder stays solid.
As for repetition, it takes 25 reps to get something into muscle memory. I like to do a new move several hundered times at various speeds. I start at 1/2 speed to get the basic mechanics, then slow it down to Tai Chi speed. I then get a feel for the movement so that I can stop it at any point and go in another direction. Once I think I know the move, I will try it at faster and faster speeds with a partner calling green light / red light until I have total control at any speed. Then I will add it to sparring, and not have to worry about hurting anybody because of my lack of control.
This all starts and ends with having a centered mind/body/soul. Do those funky breathing and meditation exercises, they are just as important as being able to perform a move.