which set of speakers should i go for?

If a speaker is overpowered, it will distort the sound due to mechanical problems in following the movement engineered for that transducer. Basic law of physics. No matter how cheap or expensive it is. If your amplifier has too much power and you turn it up too far, you get distortion from the speaker, and at some point damage to the voice coil(s). And that is assuming the gains are set properly or on the low side. A basic radio does not make a speaker distort if the speaker handles more power than the radio, it transmits distortion which the speaker reproduces. That is different. If you have a cheap amplifier, you got the same problem assuming the speakers are good quality. Chronic, late stage optimist.

ok, a few points i would like to make are: A) the gain on an amplifier has very little to do with how much power you get from an amp. the gain is a signal adjuster to match the input signals so you dont over drive the speakers. the power you get out of an amp depends almost entirely on the impedance of the speakers hooked to it. ever wonder why they dont tell you that a certain amount of gain equals a certain amount of power? if the gain was relevant to the power output then the gain would be labeled in watts and not volts. B)saying that just because a speaker is rated for a certain power level and therefore will never distort unless you supply more than rated power to it is just totally false. even though you do have a point as far as signal distortion being reproduced that still goes back to my earlier point about improper settings. more expensive speakers will be less prone to mechanical distortion because of better engineering and better materials. a regular 25x4 radio amplifier can definitely distort most speakers if you turn it up too much. speakers distort for more reasons than just too much power. cheap speakers have weak flexible cones and a very limited distance they can travel so even though they might be rated for a certain wattage they can be physically over driven with much less power.

Look, if you take a "cheap" 4 ohm car speaker and hook it to a hugely overpowering 12 volt amplifier, but you turn the gain way down and keep the head unit volume low, the speaker will have its own distortion but it is not very audible and the sound is perfectly acceptable if you can hear the music, which is unlikely in most or all motor vehicles. Turn it up, I don't care if you call it gain or not, that thing sounds awful and it isn't from the amplifier. You say and I agree that this speaker can be overdriven using a low power amplifier, and my point originally is that a lot of retail 6.5 inch coaxial and component speakers for car audio are in the "cheap" category because the market demands cheapness. Using an amplifier that claims to be 100-125 wrms/ch (which I honestly doubt is true) with a cheap speaker does what you say, it causes the speaker to distort. You seem to feel that most amplifiers are improperly installed even by a reputable professional installer, since your statements repeatedly emphasize bad gain settings causing distortion. That to me is like saying all dentists screw up the anesthesia when they give a person a filling, and everyone is walking around with nerve damage in their face, or every thoracic surgeon who does an appendix surgery leaves a hemostat inside the thoracic cavity, it is just a matter of time before you get sick and die from it. I assume most amplifiers are installed properly, especially those installed by reputable installers.   That leaves me with the premise that the distortion comes from a real bad amplifier or more likely bad quality speakers over driven by too much power.Chronic, late stage optimist.

your original argument is that a "cheap" speaker that is rated for 100W, which is theoretical, will not be able to handle a true 100W due to it being a cheap speaker. my point is that you are under the assumption that just because you hook a speaker up to an amp that is rated to supply 100W, that the speaker will actually draw 100W, which is not usually the case not matter how the gains are set. gains have little to do with power. the speakers electrical resistance is what mostly determines the power output of most amplifiers. a speaker does not have a static resistance, its impedance goes up and down depending on the frequency it has to play and also depending on its engineering. so with that being said, you can hook a 100Wrms speaker up to a 300W rms amplifier and probably still be ok and distortion free DEPENDING ON THE FREQUENCY BAND that you make the speaker play. each speaker has its own impedance curve depending on how it is engineered but in general as the frequency goes lower the speaker's impedance drops. and, as the impedance drops the amplifier is going to deliver more power (ohm's law) assuming the voltage stays constant. so you see now that the ratings on amps and speakers are mostly for show because everything is relative to the resistance of the speaker and its resistance is relative to the frequency it is trying to reproduce. a 4 ohm speaker will hardly ever see 4 ohms while playing music. i like your hugely exaggerated examples of comparing botched medical procedures to setting an amp, honestly MOST amps are not set correctly. there are no qualifications for being an audio installer and you dont have to go to school for it, i should know even my amps are probably a little off because i set mine by ear. its honestly not that serious to be a little off with your gains because your gain has nothing to do with how much power you get out of an amp. in my opinion, the reason why cheap speakers are more often blown by their rated power or less is because they are part of a cheap basic system where these speakers are expected to reproduce every frequency and arent being supplemented with a sub woofer or filtered of harmful low frequencies outside of the rated frequency response by a crossover. so even on normal power these speakers which are already poorly designed are also being tortured with low frequencies. these frequencies put stress on the speaker mechanically and electrically at the same time. the speaker has to move farther than it is designed to in order to reproduce the low frequencies AND the low frequencies present a lower resistance to the amp thus it draws more and more power from the amp. if the speaker doesnt have enough cooling features, which cheap speakers usually dont, it causes a run-away effect of lower and lower resistance from a hot coil and then POP! the speaker is no more. the only thing that can save the speaker is to turn it off for a while and let it cool. a cheap speaker will last longer being powered with its rated power, assuming its ratings are accurate, as long as it is being filtered from frequencies that it is not designed to play.