At white and yellow we look at two punching levels - one is the midsection or towards the solar plexus, and the other to the upper level (to the nose). These two heights provide a nice 'parameter' for the basic strike to allow a good amount of force to be applied to the opponent whilst reducing the probability that you're going to break your fingers on a bony corner (like the chin).
The takeaway lesson for beginners facing a moving opponent is when the opponent moves, the punching angle needs to move in relation to the target being struck. For instance, if you're punching the nose, and the opponent is bent over, you may have to drop the elbow and strike more upwards - driving more with the legs and shoulders.
Baton Instruction by Hanshi Tim White
The above video shows Sifu Tim White providing military baton training. Instead of just punching directly at the target, Sifu White shows what happens when you direct the strike downwards. Similar to aiki throws, the force is directed at a triangulation point between and behind the opponent's legs on the ground. This forces the opponent downwards and backwards, rather than just take the hit and come back for more.
Lastly, while we can take the mid and high section punches as parameters, Sifu White's downward angle of striking lends credence to the mid-level oizuki (lunge punch) from Chun-ji. What a great lesson!