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
It's hard to define NGE because it's a one of a kind series that hits everyone differently. You don't often see a series whose director said "if you don't understand it it's your problem". It's chock-full of triple-layered details you will miss on first watch, but at the same time you should definitely watch with zero spoilers the first time, for the experience.
It's very, very well made so I guarantee it will not be a waste of time, and lends itself very well to the occasional rewatch. What you take away each time and your level of enjoyment for each watch will, interestingly, be mostly unrelated to the theatrical value, which tends to remain constant. I would recommend reading up on lore and plot hints for secondary watch-throughs though.