And the biggest influence on sound quality is...

T

I appreciate 2psyop's mention of hearing aids.  Many of us (me) have compromised hearing associated with aging.  I have good HAs, a good small room system, and a very good desktop setup.  I almost never use HAs when I'm listening to either system.  I've found HAs to be fatiguing.  Without them I find that a short period of listening at low/moderate levels with small adjustments in volume until I get that just right combination of detail and air without going too loud -- which is also a problem for the hearing impaired -- puts me in a zone where I forget about my hearing and enjoy the music.  With near-field listening (2-3 feet) the room doesn't have much effect.  In a small room at moderate volumes the room comes into play, but less than in a large room that may not have been designed for good acoustics.

With live music the room is everything.  I go to a lot of concerts in Sun City Roseville , CA where I live.  The acoustics are terrible but the performances are usually entertaining but I wouldn't want to reproduce any of those acts through my system no matter how good the performance.  (Rudy Van Gelder usually isn't on hand.)  The finest hall I ever heard was built sometime around 1700 in Prague.  It is where Mozart debuted "Don Giovanni" and where parts of the film "Amadeus" was filmed.  In 2017 I attended a concert there.  It is oval-shaped, perhaps 75' x 50', or perhaps somewhat larger.  It has a shallow dome with clerestory windows that can be opened as I recall.  The sound of the piano and chamber pieces I heard was simply glorious.  If I had such a room I believe I could be content with a Bose radio, but I reckon even my desktop system's value would increase by a factor 100 fold.

I hope some well-heeled audiophile somewhere can replicate that room in one of his estate's. 

The room+speakers, then everything else. You’d be surprised how good some “bad” recordings can sound with high-end speakers in a proper room.

1. Gummie

2. Ears

3. Wallet

4. Good wife

5. Room

6. Recording 

7. Speakers

8. Preamp

9. Time....maybe that is number 1.

The last thing I changed.  (if I got it right)

Seriously, though, I'd have to say speakers.  Every time I change speakers the system gets VERY noticeably different.  I've made small, to the extent I can, modifications in the room and there is impact.  But admittedly I'm limited.  Bride has nixed taking out the wall and the stairs on the other side of it.  Also, won't let me blow out the bedroom upstairs so we can have a higher ceiling in the listening area.  MAN!

Amps have peeled back layers, brought more speed and clarity and with them nuance.  So have wires/cables.  The Holo DAC was both subtle and powerful.  The Townsend speaker bases were the biggest surprise.  They very noticeably impacted the treble, ion a good way!  Still don't understand that.  Are speakers the most important thing?  I don't know.  But I'll say, in most normal situations, the speakers have the biggest impact.