System Synergy

System synergy and enjoying the music is certainly what our hobby is all about. It is not just a matter of proper TONAL balance, but instead, discovering what components and cables work well together to compliment each other, our listening preferences, AND our listening rooms. Unfortunately, there is no "magic formula" that we can go by to determine this. There may be a few "rules of thumb" we may discover over the years that may tend to steer us in the right direction, but it is often a personal thing.
I have helped other fellow audiophiles put together systems, assisting them with their quest, and one thing I have learned is that what may sound great to one person, can often sound rather un-pleasing to others. We all have personal preferences as to what we find as either "pleasant sounding" or "correct". Also, people tend to enjoy different types of music as well, and the presentation of that music will also vary. If someone prefers hard rock, and does not have an interest in, say violin or female voice, then one would tend to build a system around that preference. I always try to get a feel for an individuals' musical taste and listening preference before making any suggestions. I would prefer to have them hear a few different systems first, and getting their reactions of what THEY hear as pleasing or not. Even my own taste tends to change from year to year. Beyond "getting started in the right direction", you just have to experiment and let your personal taste be the judge. If the music does not move you emotionally, keep experimenting until it does!

My experience has lead me to believe the best way to go about it is to find speakers that you like, but that also work in your room. Speaker to room matching is the most important thing to get right. Room treatments are critical here.
Then find an amp (integrated in my case, preamp + amp for others) that works well with those speakers.
Then the sources, then cables.

I say this because I've had some really good speakers with some really good amplifiers, but because the speakers didn't work in my room it was all for naught.

Technically it's matching impedances of source -> amp/pre -> speakers.
The general rule is where output impedance is substantially lower than input impedance.

I agree with Byroncunningham's suggestions. Start with types of music you want to play first and speakers that can play those types well, then select what will work in your room from that group.

I also agree with Byroncunningham's observations except that I think it omits an important initial step, that is determining which type of speaker (dynamic, horn, planer, electrostat) is most likely to produce the type of sound and 'sound-stage' that is most important to you. They all do it differently and what I prize may not float your boat at all. You must also assess your willingness to really work to get the best results out of the type you do chose.

Most high quality results do not just happen when you follow generic advise from reviewers and audiophiles. Formulas, to the extent they exist at all, are merely starting points and are devoid of sensitivity to personal desires/needs.

FWIW, it took me many years just to find the type of speaker that I could make work for me (that was before the Internet existed) and once determined it took many more to find the specific speaker that did exactly what I expected out of a 2 channel system set up to excel with classical and jazz music.