And the biggest influence on sound quality is...

Ultimately, recording quality and room will define the limits, but I am talking about top level equipment. In your average $50k system I am not sure which component contributes most. But I belong more to source first school, so, I guess, it's either the recording or "transport", be it turntable itself, cd transport or tape deck transport. Poor recording will sound like junk anywhere but with average recording the better your set up is the better it will sound. It's a continuum from very poor to great recordings, and I think the answer to the question is more complicated than this or that.

My ears. Have fun with it all and the experience.

The room and the system are what they are, recording quality easily the greatest variable. Now, one  can manipulate and change audio components and room treatments, same doesn't hold true for any particular recording.

This is a fun thought experiment.

If your source is LP, then I would argue that your playback system (turntable, arm, cartridge, setup) is most important.  Imagine you had near mint pressing of Kind of Blue or Aja, and you played it on a $35 Crossley.  It would sound like sh*t.  However, given a decent playback system, the recording is next.

Digital is very different as you can get acceptable sound from a modest or inexpensive source.  Here I would put the recording quality first.

Then it gets difficult.  Speakers are very important but require a suitable amplifier and proper setup in a room that they work well in.  Too many dependencies, but if I had to rank: Speakers > Set-Up > Room > Amplification.  Then comes the fun of cables, power, and tweaks.

Two separate issues are being conflated here. The recording is not a part of the system, but an input to the system, and its quality is a fixed condition beyond the listener's control. The relevant question is what's the strongest determinant WITHIN the playback system/environment.