Technique is more important than power. The punch should start at your foot and work it's way up your body, through your hips, core shoulder and eventually to the fist. It's a fluid movement that starts from a slight foot pivot and ends with your fist. You can generate a lot more punching power with your legs proper and hip/trunk rotation than you could ever achieve by increasing upper body strength. However, I'm not discounting the importance of upper body strength.
Get in front of a mirror and work on your punch in slow motion, with no power. Keep doing it until it's ingrained in your muscle memory and it becomes as natural as walking. Gradually increase your velocity, (notice I didn't say power). Don't focus on power... think about a golf swing. If you try to crush the ball, not only do you miss the sweet spot, but your using the wrong twitch muscles. You need to generate speed and the best way to do that is not to focus on power. Power will come with proper technique.
Bass Rutten has some great videos on bar room and street fight techniques. Sure, he's a MMA master, but his street tactics are amazingly effective. Here's one:
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