I think people are spoilt nowadays for instance goldeneye 007 was a fantastic game back in the day, but under huge explosions it would really chug along.

OT probably 2nd behind gameplay.

Pretty low. I mean, I love when a game has great graphics from a technical view but I think that never decided if I bought a game or not. Fps, art-style, story, gameplay and so on decide if I buy a game (which of that depends of what kind of game it is) so I would say I like it but it's pretty unimportant for the fun I have with a game.

When I see threads like "Horizon has ruined graphics for me" I can only shake my head to be honest. 

At the bottom? I refuse to believe that people would be fine playing just Atari games as long as they just had a good story, gameplay and replayability.

1- Gameplay
2- Level Design
3- Stable performance
4- Graphics
5- Music
6- Story

I don't have a list. Creating an accurate list would probably require pretty deep analysis, if a list is even a sufficiently complex representation of what I value in games. That said, it's enough for me if graphics meet some arbitrary 'good enough' level, and everything above that level is plus.

Roughly speaking, there's probably three levels of (acceptable) graphics for me: barely good enough, basic, and extraordinary (in a good way). Barely good enough is OK but might affect my enjoyment somewhat negatively, basic is whatever (doesn't affect the experience), and extraordinary actually improves the experience. Of course things aren't this simple, or otherwise I wouldn't see any value in remakes. How it works in my mind is probably surprisingly complex, and I'm not going to analyze it now since it sounds like a pain to do.

One thing I do not understand is when someone says that they value game-play highly but don't care about graphics at all. That doesn't make much sense to me. Game-play advancement is tied closely to graphical advancement.

On par with everything else, I find the idea that certain aspects of a game are more important than others a mediocre one. Every aspect should be equally important.

1.Gameplay
2.Story
3.Graphics
4.Sound

I like nice presentation.

The taste of a meal is most important but it's presentation is up there especially when you're spending money. If you go to a restaurant and the food looks like a tragedy, it lessens the enjoyment of the food even if it tastes great.

They're important to my purchase decisions in that I'd prefer my games to not look shit, and beyond that, it is of course very desirable to get a certain wow factor from a game's visuals. I mean why wouldn't you want that?

If I were to make a list, they'd be somewhere pretty low, but that doesn't make them not important. Great visuals can do wonders for immersion, and the like.....really helping a game come alive.

I don't like the idea of one area being prioritised over another, everything should be equally as top notch.

Anyway, I'd say gameplay > story = music & visuals (both compliment the story, music invokes an emotional response better than words can and good visuals help draw us into the games world).