If you really want to get to know how to do it right even if you aren't literally DIY-ing it, www.diymobileaudio.com is the best forum to browse. Basically, in a car, the basic problem is the car itself, not just the gear. I've heard cars where the owner blew $2,000 of gear on, but didn't install the speakers nor use the proper processor, and it still sounds like crap. In the meantime the budget category of the local competition scene was won twice in the last decade by a guy who used a TOTL Alpine head unit (that had the proper processor, plus a V-Drive amplifier section that puts out a real 20wpc++) and $30 raw drivers (that's for a pair of midwoofers
and tweeters).
In brief: the reason why the processor is the primary concern is because no amount of other gear can fix the fact that you aren't driving a Maclaren F1 - you will always be closer to the driver side tweeter, then the driver side midwoofer, then the passenger side tweeter and midwoofer. You need to aim the tweeters towards the center to minimize its dispersion pattern sending soundwaves to just bounce off the windshield (you can't put acoustic panels on it unless you have X-Ray vision), which does a lot to center the vocals. Ideally you should do something similar on the midwoofers too, mostly to aim it upward, so you won't have a soundtage where some instruments (coming more from the midwoofers) are set lower. Fine tuning will be done on these through the processor primarily to tweak time alignment, introducing delays to the speakers closest to you so sound from all of them arrives at your ears at the same time. When you do this however in most processors this is done in the digital domain, so when it sends out the signal, the crossover can be applied here as well, so your amps' channels get only the freqs for the midwoofer or tweeter it's driving. Some amps conveniently have five channels with a dedicated subwoofer channel to simplify wiring for such set-ups (instead of using two or more amps).
Used to be head units were 1- or 2-DIN units that you pull out and replace, but since the mid-2000s they've been integrated into the dash for aesthetics as well as for factory GPS units, so processors nowadays will use one that takes in high-level (speaker inputs) and send it through an ADC, process in the digital domain, then send them out through a 6-ch or 8-ch DAC (usually the same type as on an HT receiver). Don't worry too much about the GIGO principle here - no amount of conforming to GIGO at the cost of being able to apply time alignment and such can give you a Maclaren F1 cabin. Hooking up a HiFiMan HM801 to the 3.5mm aux input isn't going to magically simulate sitting in the center for example, so no matter the changes in tonality, the vocals will still be off-center on the dash and everything else all over the place. Even tonality can suffer because reflections off improperly mounted tweeters on the windshield, plus time alignment issues, can result in sharp treble - particularly with cymbals, or "t" and "s" in the lyrics - because you're hearing each tweeter out of sync with each other and the midwoofers.
Basically, car audio has a lot more similarity with pro audio than home audio, but for those who like working on their cars and/or joining EMMA or IASCA autosound competitions (scores based on imaging from either just the driver or both front seats, neutrality/spectral balance, etc), that's precisely where the fun is.
A couple of examples of proper tweeter mounting: