I think it's time I add my 2 cents in here....eek!
Ultimately.....don't install anything until you have everything! But I understand the itchy sidecutter hand completly. I personally feel that you should replace the speakers first. This will increase your SQ, but it will not raise your volume by anything, in fact it could actually LOWER your volume....how so you ask? Efficiency, OEM speakers are usually high efficiency speakers, now, as you raise your efficiency you also raise/lift your lower frequency handling ability, as such a HE speaker will not go as low. HE speakers take very little power to get high volume, but they sound like A$$. Hence why it takes so much power to drive a subwoofer. To deliver such low notes, they need to be low efficiency. So by replacing these speakers, you will slightly lower your volume because they handle the lower notes better then what your OEM speakers will. But, never fear, because once that amp hits them, you will get it all back plus more!!!! WOOHOO!!!
Now my thoughts concerning the "myth." IMO both too higher and to little power can destroy a speaker pretty quickly. It all comes down to the mechanics of the speaker.
Too higher power can cause damage in several ways. One way is simply adding to much power into the voice coil and melting it down and causing the speaker to seize. To do this you need a massive amount of Overpowering to occur.I showed this to my apprentice by taking a 4inch woofer and plugging it into the wall! HAHA....240 volts at 50Hz....it was highly amusing if not extremely dangerous. The other way happens over time.By feeding too much power, you force the cone of the speaker out to the limits of it's excursion and hold it there until the signal starts decreasing and heading into the negative, once it goes into the negative region, the cone is pulled back and held all the way back inside of the chassis until the signal starts going positive again. Remember this could be happening anywhere between 20 times a second to 20,000 times a second (subwoofers right through to tweeters included in this) now holding the cone of a speaker out for any period of time instead of it being allowed to move freely builds up resistance inthe voice coil, resistance equals heat, get it too hot and it will start to seize in sections if not altogether.
Now for the touchy subject of underpowering....don't shoot me please!!!
Someone mentioned earlier that Underpower damage occurs when the amplifier is sent into clippng "distortion" This is exactly correct!! Lets break down a clipped signal....it's a square wave, for all intent purpose, it has a flattened peak and a flattened trough. Now for the speaker to recreate those troughs and peaks it must be held in a one position for the duration of that "flatspot" Now bear in mind what I said earlier about holding a cone in one position, it builds up resistance in the voice coil, resistance = heat, and thus once again, you can cause overheating of the voice coil, causing sections to heat up and seize if not seize altogether.
Ok, I will breifly touch on distortion as I have rambled long enough....The human ear doesn't hear distortion until it is approxiamtly 5-10% of the full music signal, and that rating is for people such as us, who continually listen for distortion, the average person may not notice audible distortion until it is at 20%!!!! that means that one fifth of your audio signal is slowly damaging your speakers and in the case of underpowering, damaging your amplifier as well.
I hope this will clear up some confusion, to my fellow installers, please feel free to add, correct or criticise what I have said, these are only my opinions that I feel I have thought through well enough for them to be true.
Raymond Wilkinson-Reed
Check all advice given with a meter