I prefer smooth controls, great fighting, unique and useful items and really good dungeon crawling as opossed to perfect graphics and an interesting story. Even if the graphics aren't the greatest looking and the game masters all those things I said about gameplay before, for some reason I will end up loving the graphics regardless.
I don't need a great story backing up a Zelda game. After all OoT is my favourite Zelda title and it is constantly being bashed for bad character development and terrible story. Although it's my favourite game because it plays like smooth butter and the dungeons are phenomenal. A good story is just the icing on the cake for me.
Zelda has never really disappointed me with graphics or artstyle though. Whatever game it is, I usually come to appreciate the graphics and artstyle eventually so it's not really the main thing I look for in a Zelda title.
So whenever I hear that a new Zelda game is coming out, I pretty much immediately think about the dungeons and gameplay first and then I think about story. So all in all it's definately the gameplay that affects my enjoyment of a Zelda game.
Ps. Zelda music is always great so I don't have to worry about not enjoying it But if they can make REALLY great music ( Majora's Mask, Spirit Tracks ) then that is a nice extra bonus.
The scenery, music, action, and puzzles I love the scenery for example in Twilight Princess the mountains and such and the puzzles are big for me. I love a good but if it's stupidly difficult it kinda ruins the game for me until I figure it out.