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

Speaker room match
Then source
Decent amp
Cables
Isolation platforms (speaker and source) 
Power

There is a diminishing point of return on any component.   Spending more doesn't necessarily get you much better sound.   But it is the loudspeakers that you are actually listening to.  They are the primary transducer in your system

In order to get good dynamic range, the ability to play at concert levels in a good sized room, have good imaging and a truly natural tonal balance, there is no way around spending a lot of money.  But then "a lot of money" is a relative term.  

Most of your hi-end loudspeaker vendors (Magico, Wilson, Focal, Avalon, etc) have a top line loudspeaker selling in excess of $50,000.   Are they really better than a pair of KEF LS50 loudspeakers with sub-woofer augmentation?  Depends on how much you're demanding from a system.

There are solutions which are an exceptional value.   In most homes, I'd put the Dutch & Dutch 8c up against any of the $50,000+ loudspeakers.   They have astonishing imaging, clarity and a great natural tonal balance.  Damn near perfection.  But they cost $12,000, which is far beyond what many would pay for loudspeakers.  But what you forget is that they are a total system with built-in bi-amplification, built-in DSP and controlled directivity.  You could run the D &D 8c with an iPad, a hi-res streaming service and be done.   No preamp to buy.  No turntable with expensive cartridge, phono preamp, etc.  In light of that, $12,000 isn't all that bad.

Another cost effective solution to the extreme hi-end is the DIY Linkwitz LX521 system, which would run you about $6000 for loudspeaker components, cabinetry, active crossover, amplification and cabling.  Again, almost a full system.  Just add a preamp and the source of your choice.

So your question really starts with your requirements and budget.

The most Overlooked, Underrated, Un sexy Component is Power Delivery. I consider it a paramount component because having Clean Power gets your entire System working at its Optimal Performance, and then there is also the cost.

I did not start with an efficient Power Delivery system. I found that after a while I was looking for a new Power amp or Pre amp or Speakers. When I introduced Substantial Power Delivery to my system, it was like I had a whole new system. The only thing I have done since then is make tweaks.  

Speaker to suit the room first.  Then amp to match the speaker 

For me, the preamp is of ultimate importance. Everything goes through the preamp and each sound is shaped by its character. The preamp is the "first watt" that creates the overall sound of voices and instruments and creates the soundstage's width and depth. Not that a good amp won't help, but I think the preamp is fundamental.

I have a twenty-year old ARC Reference 2 Mk. 2. I'd buy a new ARC preamp if I had the money. Yet I do love the one I have. My SMC Audio amp (McCormack DNA-1 upgraded) and ARC preamp will sound excellent with most speakers.

Obviously I have chosen a certain type of sound to create what I think of as musicality. Opposite, I would say, of Dynaudio and Krell. I have not heard d'Agostino equipment, but I assume it has the powerful punch of its predecessor Krell.

Although I would say that my preamp is known for its soundstage and positioning of instruments, I do not need to hear each note isolated in its own space. I have had seasons tickets to the L.A. Philharmonic for years and live music does not sound so clinical.