I would like to propose a method of classifying marksmanship qualification standards. The four very broad categories seem to cover everything I want to discuss.
Untrained Marksman, someone who is not proficient in using a battlesight zero.
Trained Marksman, someone who is proficient with a battlesight zero.
Skilled Marksman, someone who is proficient to the maximum effective range of their weapon.
Sniper, a Skilled Marksman who possesses the other skills necessary to serve as a sniper.
Please note that the worst guy at a High Power Match who scores "Marksman" is still going to have a better training base than the guy who never shot beyond 300 meters on an Army pop up qualification range. That is the difference between a Trained Marksman and a Skilled Marksman. Also note that a Skilled Marksman and a Sniper can be firing at targets at the same ranges, and the effective difference is one of "value added" skills that a trained Sniper brings to the fight.
But getting back to training focus. Training for CQB is easy. You can do it with a rifle, pistol, bb gun, paintball marker, or airsoft setup. This is not where you should focus your training. CQB falls well inside a weapon systems battlesight zero. A "Trained Marksman" should be proficient at CQB, but a "Trained Marksman" should be working to become a "Skilled Marksman" instead of a CQB expert.
So you ask, "Where should you focus your training?" Traditional long range marksmanship. Standing, kneeling, sitting, prone unsupported. Why should you do this instead of working on CQB techniques?
Skill. CQB is a single direction skill gain, it gives you nothing but CQB. Traditional marksmanship training on the other hand improves everything else. The skills you learn practicing traditional rifle marksmanship translate into faster target acquisition once you do need to fight at CQB distances. CQB training can destroy your long range accuracy, mainly because of trigger control and precise sight alignment. When you train to rush a shot to get fire off before an enemy can fire back you are training your muscles and brain to rush the shot.
Logistics, mainly money. To get truly good at CQB techniques you have to shoot a lot. Hence the preference for using something cheap like a 22 long rifle analog of your main weapon system, paintball markers, or airsoft gear. You can burn out a barrel of a rifle before you ever get truly proficient at CQB. In peacetime one of the Rangers I went through SFAS with had burned out 2 M4 barrels in 18 months with the Regiment. That is the type of training you need to be truly proficient. The rest of us are constrained by budget and get "good enough" to be better than the guys we are going up against.
Tactics. If you are the underdog in a fight CQB should be part of your "escape and evade" skill set, not a part of your "attack and destroy" skill set. If you close with a larger and better equipped force the odds are already stacked against you. No matter how good you are at slicing the pie around corners the other side will win in the end. Using an M4 for CQB is fine, but I want to shoot the bad guys from as long away as I can get and still put steel on target.
There are a lot of venues to train. High Power, F-Class, Palma, and "outlaw" sniper matches are great for long range marksmanship training. If you don't know how to get started go to an Appleseed and learn all you can there. On the other end of the spectrum USPSA, 3-Gun, IPPC matches are all great for CQB style training. Yes the folks who focus solely on short range CQB style stuff will be faster than the folks who focus solely on High Power. So be familiar with CQB techniques, but focus your training on accuracy, because only accurate fire is lethal.
In both Iraq and Afghanistan the vast majority of insurgents fall into the "untrained marksman" standard and the heavy reliance on things that blow up shows this.
Below are some articles discussing insurgent marksmanship.
Afghan/Taliban marksmanship, which really explains why they rely so heavily on IEDs.
Taliban Sniper fire put into context
The sniper war in Iraq, American view.
The sniper war in Iraq, Insurgent view.
A good post about gear not making up for a lack of skill, Army SDM training.