Everyone here has made some very good points.
There have been many good points made in this thread, some that I've never even thought of and I have been in a firefight. The bottom line is, everything is situation dependant. I've always been trained in the force and violence of action department, so movement there is always required. Of course, I do cordon & searchs and hard hits for a living, and I have the finest supporting arms in the world that I can't even use because of collatoral damage and the "hearts and minds" thing. But I do have a whole squad/platoon supporting me, and we have belt-fed weapons providing suppresion fire while we move. We also prefer fire and menuever to fire and movement. All of this really doesn't apply to a someone with ccw. There will be times, when you have cover, that you will not move. There will be times, when you are in the open, that you will (or better) move. Most would pop smoke and run while firing to cover their retreat. That's fine. I personally (because I have seen it work well) would probably advance as I fire, because if done properly and violently enough you will petrify your assailent to the point where they can't function. There are a thousand schools of thought on this, but most of the time you have to move to survive (especially if caught in the open). I am a strong advocate that you should always fire while you are moving unless there is a chance of hitting civilians.
So... we have basically all come to the conclusion that movement is good. What we are not in aggreance on is how to move, where to move, ect. I'm sure someone is going to come up and say I'm insane for closing with the target. Even the military trains for one on one engagements (when we do mout and room clearing), and they train to close with the enemy obliquely while firing on the move. Marine Corps enhanced marksmanshep program (EMP for those who know what I'm talking about or have heard of it, which was invented by my old Battalion Gunner) covers dynamic movement while closing extensively. That's what I've been taught to do, and have done.
SNB's system, which I have not studied extensively, may be another viable option. I know for a fact that he is well versed in dynamic shooting from the following statement...
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also see a need to be able to get hits with your toes pointing the direction that you are moving. This type of movement has your upper body working independent from your lower body, "like a turret of a tank." Toes point the direction you are headed, body turreted the direction that you are shooting.
I've heard some other very logical options. Everything is situation dependant, and probably the most important part of this thread that everyone has taken away in this
#1. Dynamic Firing is an important skill that anyone who trains to be in a firefight should cover.
#2 Movement+fire= higher probability of survival... Stationary+careful aim+slow steady squeeze= certain death.
#3 Training is the key. Train to fire while closing. Train to fire while retreating. Train to fire while moving obliquely. Train to quickly eliminate a stoppage. Train to... Train for every situation you can think of, but prioritize to fit your needs.