Sorry, I was falling asleep when I wrote that last post and completely forgot about this. Here are my recommendations for some good story anime, in no particular order:
This is quite possibly the best thing Japan has ever made. If you've never seen it, you need to watch it immediately.
This one is only six episodes long, and you will probably not like it the first time you watch it, particularly if you don't watch a lot of anime. It's very bizarre and parts of the story are borderline nonsensical. However, I recommend watching through it at least twice, because once you get past the weirdness it's actually a really well-told story about early adolescence. Along with Cowboy Bebop, it also has probably one of the best soundtracks of any anime.
>Record of Lodoss War
This is a now mostly forgotten gem from the 90s that is nonetheless worth watching. It's basically just an animated version of someone's Dungeons and Dragons game, but its fun. There is also a second series called Chronicles of the Heroic Knight, which basically tells the same story with different characters, and even more confusingly overlaps with actual events from the first story. But both are good.
This one is actually somewhat redpilled in that it explores a world in which UBI exists, and shows the kind of atomized, purposeless, friendless lives that humans would most probably live in a world where all their basic needs are provided by government and people mostly communicate through virtual reality. A covert group of survivalists rebells and forms a self-sufficient community that refuses all gibs from the AI government. If I remember correctly it gets pretty bizarre towards the end.Post too long. Click here to view the full text.