What is most important part of a system?

There are so many variables that this equation is unsolvable.
Different - expectancy, taste, room etc. etc. etc.........................

But I suppose that most will agree that there are no point to buy an expensive source if you have a mediocre preamp.

My suggestion is to start building your system from speakers to up.

plutos one pair of transformers in the preamp.  As good as the preamp is, the DAC made more of a difference in every system we installed it.  In some instances it was night and day.  We were stunned at that - the light was off and then the light was on kind of difference.  The sound of the DAC was transforming no matter what speakers, preamp, amp or cables.  Same goes for our phono stage.

Happy Lisening.   

Speakers

It should be obvious to anyone with ANY electronics knowledge at all, that not all parts are critical.  The critical parts are the transducers, e.g. speakers and cartridge if analog.

This why the advice to put half of the budget into speakers is both common and good.  Room treatments are also critical, but are not electronic - they will require some knowledge of acoustics.

The amp needs to be able to drive the speakers, which can be difficult if they are highly reactive or require high current delivery.

The pre-amp is a control center and at the high end can enhance certain euphonic characteristics (tubiness).

The DAC is easy to get good sound from at a few hundred dollars and there is no need to spend $35,000 on it.

But $35,000 spent on speakers can be very worthwhile -- unless you buy Magneplanars for $6,000 and like their advantages over their dis-avantages.

The "Chairman" of anybody's system is indeed media:
It could be fantastically recorded mostly classical, jazz, folk or it could be poorly recorded rock or combination of both 
One way or the other, no tunes to play -- no need for other components unless you're stuck to your tuner or playing your guitar via microphone :)

To that owned recorded media, the listener should than take first most important step to find synergy with system that one is about to build of course having budget in mind weather it's limited or not (just like in case with ebm :-) 

Categorizing importance and quality of components is deep error IMHO, because at least each an every separate component has dedicated function. Finding components in proper synergy within the budget is far more important PART than having single component as most or least important part of your system. Therefore the sound system that pleases you have importance of ALL components logically EQUAL unless you wish to literally define amplification components as secondary importance. You can therefore connect your $5k speakers directly to the output of your CD player with no volume control, because it ain't gonna be to loud anyways :-) Also in case with analogue -- not even phonostage or even speakers important(you may logically assume) -- just position your ear as close as possible to the needle or lean it firmly against the stand and you will be able to hear tracks. Why not? At least we will have golden ears evidence haha ! :-)