What is the most important component to consider while building a new system?

FIRST; The right domestic partner or at least an animal friend. Mountain Gorilla is a little tough on some gear.. Maybe a terrier..

Then pick what ever you want.. Won’t have to navigate the narrow path of domestic bliss behind some MAN purchase vs WOMAN purchase vs Gorilla vs Terrier purchase..

SECOND; Speakers and room, or room and speakers. Either way.

THIRD; To get started (an option) I went out and powered 2 serious speakers including the bass section with two 59.00 2.1 class d and a 79.00 dollar tube head set/dac/WiFi/Tone control and everything else under the sun. Thing.

I was floored, just floored.. I used a Galaxy S3 for a source.. I did use really good cable though.. :-) Smart a$$ neighbor blabbing about how class ds were junk.. Shut him up.. 200.00 wonder system..

The amps were 50x2 & 100x1. The bass (100), mids (50) and highs (50).. The heaviest part was the cables at least 3 times the weight of 2 amps, 1 preamp and 3 PS.

DIY like me on the room and DIY some gear/speakers/cables/things/stuff/do-dads..

I did buy a new phono/tape pre amp, second new purchase in a long long time. The first went back.. I always by used..

New Parts.. Used Gear.. Fast women, (not to fast) ;-)
Regards

Setting up the system correctly in your room and making sure your whole system gels with your kind of music is the most important part of your system. Also i would say playing good recordings is an essential part related to this.

Some will say the room, some speakers; I think both. 

Like Paul I make some portion of my money selling electronics or at least designing them I totally agree the answer is speakers. No I would say to more important things are the room in the recording/mastering but those are not part of your “system”