Well, if you care a lot about a solid story, then Gintama isn't for you. It may not have a whole bunch of that filler material, but it's more about characters than anything else. Its comedy is also heavily Japanese-centric, whether it's people, other anime, or the culture itself. Just going off of what you said, it seems like you want an anime that is well-animated, well-paced, little-to-no filler, and has a good engaging story. I mean, sounds obvious that people want those things, but I think if you want something like that you're better off going to a 12-24 episode anime, or one that isn't over 100 episodes long.
And that's what I am doing. 24 episodes are more than enough. If the series is longer, than I can wait one or 2 years for the next season as long the overall quality is good.
Everything that is better than this:
Classic lazy animation. Also seen a lot in One Piece.