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

1) Speakers. 
2) Active or Passive
Then start building

I would definitely say it is the speaker first, especially in these times when there are many streaming based digital sources (D/A converters) with very clean and low distortion sound available for a reasonable and modest sum.  Not like the old days when tuners, record players, cd players could sound very bad.

Speakers and or DAC

I would choose the speakers to fit with your music taste and your room size before anything else.

Everything involved impacts sound quality.

So what are we talking about here? 

Are we starting from scratch with a completely empty room and a fixed budget?

Most times, people already have equipment and are desiring to upgrade.  If you aren't happy with your speakers, then go down the speaker path (really difficult).  Then you find that your existing amp doesn't match well with the new speakers and you start down the amp path.  Now, that existing pre-amp isn't quite up to snuff with the new amp and guess what?  new pre-amp.

Digital source (CD transport, DAC, music server/streamer) another long upgrade path.

Don't even get me started on an analog system (turntable, arm, cartridge and phono stage). 

And then you have cables.

It is not an all in one path, it is a timely point by point, piece by piece upgrade path that takes a long time, a lot of money and hopefully some fun along the way.

So, in my opinion, the most important component would be where will this stuff be placed?  what does the room look like?  acoustics?  Also, how does the buyer like or appreciate music?  Background music only?  or will that person actually sit and listen and appreciate music and real instruments?  not a one size fits all scenario.

interesting subject, but not a simple answer.  What is the starting point, what is the budget?  where will the equipment be placed (room)?  all new equipment? or piece by piece upgrade?

enjoy