Do you belong more to souce first or to speakers first school of thought ?

Generally speakers first, then match rest of components.

Speakers interact with the room, which should be a significant consideration..

OK< I'll bite. Speakers first...but it all matters.

fuses first, then cables...eventually the rest of the system will fall into place. room last.

It is not a matter of debate. The room dictates speakers to some degree and the interface between the two makes up 99% of the sound quality the system is capable of. Next is the amp which has to be matched to the loudspeakers. Everything else is trivial. 

@hilde45 I hope that is tongue in cheek.