For optimum sound quality i would not advise going with that infinity amplifier. (Btw Infinity amps are JBL in disguise, they are both manufactured by Harman)
The THD levels are way too high:
50 watts RMS x 4 channels + 150 watts RMS x 1 channels at 4 ohms and ≤ 1% THD + Noise 60 watts x 4 + 300 watts x 1 at 2 ohms, 14.4V supply and ≤ 1% THD + N2
≤ 1% is far too high, which is the main problem with the car amps today. My old alpine 3552 has complete full specifications regarding power:distortion, and to be honest its the best car amp i've ever heard. (35w x4 at 0.04% THD) You can probably get better than this, but i very much doubt that it'll be in the form of a brand new amplifier. Your NAD C320BEE runs at 0.03% THD which is excellent, so as you can imagine that infinity isn't going to be a patch on your NAD. Going for an external amp is a good idea as the amplifiers built into the headunits are even worse.
My advice would be to look at second hand amplifiers that are slightly older since they were built around sound quality rather than giant power outputs. The V12 series alpines have almost always run at 0.08% THD, the newer PDX alpines are like everything else these days (circa 1%) so avoid them aswell. The best alpines have just a four digit number with no three letter code. (I only really know alpine, but i know that there are other brands that are equal or better, but i'm working on max sound quality minimum cost. Got all three of my alpines for less than £70 (two 4 channel and one 5 channel), although i inherited the 3552 which i am keeping as a spare at the moment as it needs some new parts for the switch mode psu)
Have a look on
ampguts to get an idea of specs. (most of these are accurate, but some are missing spec)
Another thing to look for if you're after good sound quality is an active cross over to replace those passive ones that component speaker sets come with. Here's the one i got, only cost £25 too.
That will allow you to fine tune the levels on individual speakers and their exact crossover frequencies. You'd only need one of these if the amplifier you go with does not have one built in.
As for speakers you can get almost anything, if you get an active cross over. Just look through the thiele small parameters and get what-ever is best specified. Just pay attention to basket/magnet sizes as the speakers may not fit in the stock holes. As for subs, i built myself my own 6 years ago for my home cinema, using a 10" driver and a 42 litre cabinet with a port tuned to 35hz. Have to say it is surprising how good it sounds with virtually all types of music, even classical. I won't bother saying who makes the drive unit, but i will say that it has astonishing sound quality for the price i paid, and it has lasted 6 years permanently on without any issues. (it even came complete with a full spec sheet including thiele small parameters, which is very rare these days, TBH i like it that much i've been trying to find another one, damn shame they stopped making them) Best thing to look for is large x-max (cone excursion) large surround, without any fancy shapes molded into it and make sure the surround is made of butyl rubber or similar. (much hardier than that foam crap they sometimes use, i've had a foam surround disintegrate with age)
As said somewhere above, for a really good system you'll need to have a fair amount of sound deadening material fitted, to reduce the amount of external noise.
With respect to cables so long as pre-amp phonos are shielded and routed as far from the power cables as possible you'll be fine. Amplifiers really need a minimum of 8 gauge cable, especially if talking 30amp or higher fusing, same thickness cable is needed to earth the system. You can use the same speaker cable that you use in the house for the hi-fi, though it doesn't need to be expensive just make sure the cables are routed away from power cables again.
Hope this helps.