edit: feel free to reply no matter how old this thread gets!
I'm not particularly into anime, I like it just as much as live action shows or other types of animation. Having said that, I feel like watching some and I'm not sure what to pick.
Here's a list of other anime shows I've watched/manga and novels I've read, so you can better judge what to recommend. ( would greatly appreciate the story to be completed, I hate waiting years for closure) :
Full Metal Alchemist, Naruto : both great stories, I've read the mangas and loved them. They wouldn't be a priority to watch because I already read them.
Attack on Titan: started with the anime, it was great, switched to the manga, got extremely disappointed with the story development and its ending. It felt a bit like nonsense for me.
Dragon Ball/Z : probably my favourite, I've rewatched it recently. I don't like GT and Super.
Overlord: I've read good part of the novel and manga. I'm liking it so far
JoJo's Bizarre Adventure: please No thanks. Not for me.
Death Note: loved the first arc, not a fan of the ending but no hate for it unlike with AOT.
I also recall Escaflowne and Inuyasha, they were alright but not something I've loved or hated. Cowboy Bebop also in this category, excellent visually and great OST but the story wasn't as gripping.
Other than that... Feel free to suggest any other titles! Extra thanks if you are specific about any versions and why is the show so great.
I'm gonna take some leaps
If you like the mind games parts of death note (since you seem to like the first part)
I recommend trying Kaiji. My personal fav and one that got me changing my expectation of anime.
If you like DBZ I assume it's the fighting. And even though the first assumption is people who like Anime probably will hate sports , sports anime are usually just tournaments for battling. If you want superpowers, I might recommend Kuruko No Basuke. I you want Mind Games, maybe One Outs. If you want something more modern, Haikyuu is a good shout. Classic sports anime would be Hajime no Ippo
A general shounen? Fate/Zero is pretty safe to try.
When it comes to recommendations, realistically there are lots of great anime movies to give yourself more context for what to watch
Ghost in the Shell
Akira
Castle of Cagliostro
Kara no Kyoukai
Nausicaa Valley of the Wind
These are all just based on what you've mentioned but they're still a lot of spectrum for anime you could enjoy but haven't tried
Thanks. You are spot on with Death Note, let me add I like the supernatural elements too. From DBZ, I also like the characters, the worldbuilding and how the plot progresses. I'll keep in mind the recommendations, I haven't heard much about Kaiji before asking here. Movies : yes, I've watched and liked all those listed except for Kara no Kyoukai which I had no idea it existed. I just asked about series because I felt like engaging with long format storytelling.