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.
TIA
Haven't seen these mentioned yet:
This is one of the newer shows made by Shinichiro Watanabe (Cowboy Bebop, Samurai Champloo). Follows the crew of a small terrorist organization as they implement their various plots - lots of intrigue that makes you want to keep watching.
Follows a boxer's journey in a semi-dystopian future. Very mature and themes of adulthood, especially season 2. And I mean real life mature, not gore and titties. I've never watched an anime that I found so relatable as an adult human being. Music is also extremely top tier and I'm personally a huge fan of it's animation style.
You are right, I think you are the first one suggesting these two. Thank you!