Well, great question. But there is no easy answer. While components must be technically compatible. For the last fifty years I have chosen components and generally looked no deeper into technical aspects than watts per channel, current of the amp and sensitivity of speakers. While you can get into additional parameters… typically they don’t get you very far in terms of sonic compatibility and synergy.
Getting a compatible and synergistic system is about pairing like sounding components that are in line with your personal tastes… and your personal tastes are likely to change over time as your listening skills and appreciation evolve.
Getting knowledgeable on the subject can be accelerated with study. First I recommend Robert Harley’s book, The Complete Guide to High-End Audio. This addresses listening terminology, components and system building. Subscribe to Stereophile, The Absolute Sound, and HiFi+. Learn to read in between the lines. And listen to as many of the components as you can, reading reviews on them.
There are broad categories of high end sound quality. There is the muscle group (similar to the muscle car lovers), powerful, loud and dynamic (MacIntosh / B&W), there is highly nuanced sound with a huge sound stage and good slam (Boulder / Magico), there is really showy flashy high end sound, holographic (Rowland / Wilson), sparkly showy / brassy ( Luxman / Focal (?) ), and highly musical warm natural sounding (Audio Research, Conrad Johnson / Sonus Faber) systems. I am sure there are many ways to cut this.
One thing I have noticed is that people tend to have systems that reflect their personality. So it doesn’t hurt to look at who you are. So if you own a Corvette then you are probably going to be going to appreciate a powerful sounding system, if your highly analytical, then a very detailed system so every nuance of sound is in your face. If you are pretty laid back (like me) and into realistic musical reproduction then the latter category is like to please you. Also, most folk tend to move toward the latter category over time. I started off in wanting details and slam, then huge images, and finally highly musical (with details and imaging)… with realistic presentation.
One danger to try and avoid is getting, say a really detailed trebly first component (for instance a sound source ((streamer / DAC))), then to adjust for its over sparkly presentation you get a really warm rich component (say preamp)… then to balance them you get a trebly amp with not tremendously detailed speakers. This is a signal path where each subsequent component subtracts more sound quality. It is preferable to have all components voiced similarly. For instance my main system is all Audio Reseach with Sonus Faber… they are all of the same voicing… natural and musical. As I dropper each additional ARC component in I got greater synergy.