I think music = characters > story >> gameplay.
I am aware this is an unpopular opinion, but a fantastic soundtrack is definitely essential for a game to be great, for me. The less impressive is the music, the less likely is for me to remember a game fondly months and years after playing it. Characters are important because without good characters, a good story totally falls apart. Plus, who doesn't like having interesting characters in their games? Crazy people, I tell you.
A story is needed for the game to be memorable. It doesn't need to be an epic story (I am easy to please), so long as it isn't abysmal like the story in say, Fire Emblem Awakening, I am good. I used to think story in games was pointless, but after playing 999 a few years ago, as well as Ghost Trick, my perspective changed completely. I can still play and have a good time with storyless games, but the experience feels empty and lackluster, in the end. For example, here are a few games I played since last December:
Super Mario 3D World
Shin Megami Tensei IV
Zero Escape: Virtue's Last Reward
Phoenix Wright: Ace Attorney
Out of these four games, my favorite is easily Virtue's Last Reward. And why? Because of the story, characters and music. The gameplay? It is really lackluster, there are puzzles in the game, but I hated most of them (probably because I am not smart enough to solve them). Then, comes Phoenix Wright, which is weaker in the story aspect, but as strong as VLR when it comes to characters. I am in love with the Ace Attorney characters
Then, it comes SMT IV, which is way less story-oriented (although, comparing to older titles in the series, it has quite the focus on the story), but still great and memorable. And for last, comes Mario 3D World, which is fantastic in terms of gameplay, but only decent in terms of music and awful in terms of story and characters (I am sorry, Mario, Peach and Bowser might be classic characters, but they are still terrible characters).
Hell, after Mortal Kombat (2011), I am convinced that even fighting games require an interesting plot. One of the biggest issues I have with Super Smash Bros. 4 is how barebones it is in terms of single player content, that including the removal of a story mode, which was present in Brawl. Don't get me wrong, I think Subspace Emissary wasn't that great (gameplay-wise, I mean) and I wouldn't want it back in Smash 4, but a story mode with comic books-like cutscenes or something like that, would have been appreciated. Oh, well.
So, yeah, nowadays I do care a lot about story and the OP, I can't agree that gameplay is more important. A game without a story isn't worth my money anymore.