And the biggest influence on sound quality is...

1. The room. A modest system in a great room can sound great whereas a great system in a bad room will sound worse - the wider you open the window, the more much flies in, as the saying goes.

2. The system - at the risk of repeating myself across various threads, systems are called systems for reason - it is the quality of the individual components but also how they do or don't work together as a system.

Recordings are what they are. A great system in a great room will make a bad recording listenable. A great recording on that system in that room will sound wonderful.

A great recording on a bad system in a bad room will sound "meh" at best.

It is the whole system which, of course, begins with the input and ends with the room. But like any chain every link matters. If any link fails the system fails. But in some ways the input could be thought of first. The rest of the system is basically set. Changing any part involves time, effort and money. A lousy source is easily replaced.

But let me throw out another thought. After over six decades of audiophilia I have come to believe the one characteristic of sound most important to sounding real is a system is dynamic linearity. And I don't mean the first thought of what usually comes to mind which is the ability to play loud cleanly. This is part of dynamic linearity. Dynamic linearity is the ability of the system to accurately, linearly, follow the source(which hopefully albeit too often isn't dynamically linear). It's the ability to make linear level changes whether the change is micro or mini or midi or macro. Think of a live, unamplified orchestra. Change your seat and the frequency response changes and yet it still is live. Or think about listening to acoustic music at the door outside the room. The sound is significantly affected and yet you know it's live sound. It's dynamic linearity.

These days, I find myself focusing on well recorded music. With access to so much content, why waste time trying to make a turd sound good.

Room 1st which includes dimensions and treatments.

system synergy 2nd - from cables to matching amp to speakers.

3rd is speakers sized for the room. You don’t want small monitors in a 30’ room and you don’t want large Wilson’s in a 10x10’ room. I had large speakers in a dedicated room within a room 27’ long with 15’ ceilings. I moved to a smaller house and tried the same speakers in a 16’’ long room with 8’ ceilings, great speakers in a large room to terrible sounding in a much smaller room. 
 

Right behind the speakers are the amps/dac/preamp all spec’d according to the value of the speakers. Your not going to spend $2000 on an amp if you have $100,000 speakers and you wouldn’t be spending $100,000 on an amp and dac if your speakers cost $3500.

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.