Gameplay is obviously the most important part of a game.

It's all about the story for me, which is why i don't do multiplayer aspects of games.

I was tempted to remark the fact that, as a fundamental pillar of videogame design, graphics are indeed a necessity, as games wouldn't be able to work if they lacked any visual representation (the other two pillars, as I consider them, are the source code itself on which the game works and become playable, and sound/audio representation). Ultimately, the way the OP posed the question, I don't think he was asking inherently over which is more important in the raw design scheme, but which one do you favor the most, being both present on the equation: a more fluid, eye-pleasing visual representation or a catching, moving plot that make you care for the events outside the gameplay system itself.

There's also the thing that every game actually features a "plot", either explained in it or deduced by the player himself, as subconsciously we always try giving context to everything and fill in the blank spaces. Space Invaders, for example, inadvertedly gives us a basic premise of "we're (probably) defending Earth against a bunch of aliens" in its title, which in itself becomes the plot of it, regardless of whether it is told or not. Something as basic as Dogfight! for the Magnavox Odyssey can led both players to believe that there's some kind of war going down and there's this plane causing havoc, so the other pilot, being from the opposite war team, is going to hunt it down. I'm certainly going a bit off-topic here, but since I liked the way you posted this piece, I just wanted to reply about it.

Well higher quality of graphics and 60fps are not same, with 60fps game runs and feels better.

Wait where is GAMPLAY???

I Guess it is just a graphics Vs Story comparison otherwise handheld games without strory would be always bad due to the lack of graphics they have. Anyway 

Gamplay>>>>Graphics>story

I think it's a combination of both, this is because my favorite game is ffvi, for the time it had amazing graphic and and incredible story, this made this game one of the best in history

Neither. Gameplay beats both.

I think it really depends on the game and the situation. Bad graphics don't usually have a negative impact on a game unless they're done in such a way that makes it hard to see things and therefore artificially adds difficulty to a game. If a big focus is on story, then yes, story is more important. Take Shenmue for example. The story (along with interacting with everything) was what engaged players. That game could have gotten away with Sega Saturn graphics and still have been just as engaging.

Both are very important, but story is a little bit more important (let's say 65% story and 35% graphic).
Most important thing for me is gameplay though.

My limited understanding from the internet is that it depends on what ones plastic box says on it.