And the biggest influence on sound quality is...

Your system, the whole thing, including the space you're in, is essentially a transcription device.  The synergy there, e.g. the speakers to the space, is something you can optimize.  There is basically nothing you can do about the stuff you are transcribing, maybe outside of cleaning a record.  There are bad recordings of historical importance that can still be enjoyed and listened to, if you're into that, but otherwise you can go more for audiophile quality stuff. I can go either way, but as time passes I find myself more irritated by the simple placement of instruments and the failure of the recording engineer.  As for yourself, the synergy of your equipment is more essential than any individual item, and you're likely not going to get there anywhere near overnight (although it's fun to talk about).

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.