Classically punches and other hand strikes are the most common opening attack in combat, and the most frequent strike.
Hand Strikes are advantageous over kicks because they allow the legs to focus primarily on movement and stability, when you kick you sacrifice your balance to a degree and punches are easier to couple with moving forward, backwards and are more easily abandoned for running away. Finally the primary target for fight ending attacks tend to to be to the head neck and torso and the hands are generally closer to those target then the legs allowing for quicker attacks. Generally our first reaction when angry is to want to punch or slap somebody in the face.
Like kicking I find shadow boxing a great way to warm up, while punches do not have the same mobility demands as kicks, work on the footwork and set up for punches, rapid combo’s and training to develop power in the strike all tap into our capacity for speed, reactivity and power, and specifically tie the lower body to the upper body. Power generated for hand strike comes primarily from the legs and hips.
Developing a good set of hand striking skills is not just good for self defense, like dancing it can be practiced anywhere with no equipment. My go to movement pattern when taking a little play recess from work is shadow boxing.
Here is nice video of my favorite Muay Thai fighter practicing some shadow boxing for inspiration.