I don't put the actual story at the top of my priority but the gameplay, and the atmosphere. Day Z has no story at all-but it is the most immersive and atmospheric game I ever played. A good story is good and all, but I also like a game with minimal story and lets you 'make your own story' ,.,..eg, dark souls, State of decay, day z.
After playing on good PC for some months- I actually much prefer to play at 1080p, and at 60 FPS, which if your playing a shooting/action game- then yes , the 60 frames per second and higher textures Definetly help you play, aim and control better, which makes the gameplay better. Graphics and input (controls) have a massive effect on gameplay and enjoyment of the game. playing at 30fps feels laggy and stuttery now and that has a negative effect on the game. Of course depends on the game / genre. Horror game with single player much more important to have a good story. Multiplayer/ co-op game, is more important to have good servers, good map design, amount of players in a lobby, aiming and shooting etc.