And the biggest influence on sound quality is...

My experience is the quality of the recording is at the top of the list. You can’t make bad engineered recordings sound good regardless of your room or system IMHO.

The quality of the recording itself.

Then the room, the setup, the speakers, and lastly the  front end.

Try playing your speakers outside and see if you reevaluate the importance of the room. ;-)

+1 @knotscott 

I took your question to mean building a system, so I would answer absolutely

the speakers and the speakers........

With the room a close second.

Regards,

barts

Less than stellar recordings you can make better using for example the Charter Oaks PEQ-1. Would not live without it. An amazing piece of gear IMHO. 

I know it's the room but when I told my wife I wanted acoustical panels on the ceiling well then................