Elvis:

When you say that you don't want the amps to be visible, do you mean from anywhere, or just from the outside of the car? If you want a truly stealth install, meaning one that cannot even be seen from the trunk, you want to make sure that the amps you choose don't run too hot, as they will probably be somewhere with less that perfect ventilation.

As for amps, all you really need to do is find an amp that puts out the power your speakers require. You mentioned that "an amp that is all about changing your heart rhythm isn't for you". There's not really any such thing - I mean, class AB amps are best for your soundstage and class D amps are meant to drive subs, but beyond that, it's not like a particular amp is designed to have more "beat" than another.

All solid state amps will sound basically the same. There is no need to worry about high THD on any particular amp, as even most crappy amps have THD so low as to be inaudible.

Ok, so what you need to do is match your amp to your speakers. The problem with that is the fact that you can't really trust the RMS ratings of an amp. Very good companies tend to underrate their amps, while crappy companies tend to vastly overrate theirs. Your best bet is to check out the car audio forums for opinions on any amps you might have your sights set on. I could recommend an amp for you if you knew how much power you will be needing.

It was stated that you should audition speakers before buying. This is true, but unfortunately if you limit your options to what your local retailers carry you will be missing out on many products that may be vastly superior to what your local shops carry. For instance, Crystal Mobilesound makes a set of incredible components that for $119 will blow away sets costing three times the price. Problem is, good luck finding them at a local shop. Online is pretty much your only option.

One thing to keep in mind with your speakers is that the overwhelming majority of audiophiles recommend putting all your money into the front stage and eliminating the rears altogether. I must say that I agree with this. Ditch the rears, you'll never miss them.

Do you plan on adding a sub? You don't have to be a basshead to need a sub - the size of the in car speakers is just not enough to reproduce the lows in your music.