Don't care about story at all. Gameplay is king. A good story is a nice bonus. Same as fancy graphics. But both aren't needed.

You didn't start with text adventures? A lot of games were nothing but story in the early days.
Grim Fandango has bad gameplay, it's one of my most favorite games ever because of the writing.

I enjoyed both back in the day, from rogue to sierra adventures, still do. Both have come a long way.

I can enjoy cinematic games a lot, but they usually have very little replay value imo. I love The Last Of Us, but Ive only beaten it once. Will probably beat it again some day, but I need to forget a lot of the story first. Games like Uncharted 1-4 Ive beaten once and that's enough for me.

For me, it depends on the kind of game. A Point&Click Adventure without a good story is terrible, while a platfrmer doesn't need story at all.

A bad story can ruin any game, though (if the game focus too much on it).

It depends on the game. I like choice-based games like Until Dawn or Telltale games. They obviously need a good story to shine. And they feel more "honest", they're cinematic games, and they don't try to cover that fact with a awfully weak gameplay.

Normally, I prefer gameplay-based videogames. Because if I want good stories, I have other media to get them. What differenciates videogames is gameplay, obviously. And it kind of saddens me a certain trend to "movie-like" games. Some of them are good, but I feel that there are an awful lot of them lately