Depends but generally for me it can be different things. General rule of thumb, if the story sucks butt I'm not going to be interested. If I know there isn't a story then game play is huge. For example I love Kingdom Hearts, but can't play re:chain of memories because the card system is terrible. And graphics don't have to be the highest tech for me but so long as they fit the story.
Depends on the game? But it's either gameplay or story, with gameplay edging out a bit more between the two. If the gameplay is so bad it makes it difficult to play, not even good story will make me want to get it. I'll just watch a playthrough or read the wiki or something. But I can play something with decent gameplay even if the story is goofy or minimal.