Attack on Titan is definitely good. There is a lot of shock value in that first episode, but there is actually a pretty interesting world there as you learn more.
Deathnote is solid from that psychological thriller perspective. If you like that then you might also like Code Geass. Classroom of the elite is another, though a bit less serious. All of those series have the common theme of character's trying to constantly one up others from behind the scenes.
One other general recommendation is Kino's Journey - The Beautiful World. It's very philosophical but in a way that is easy to watch.. There are 2 versions, both excellent, the newer one (from around 2017) is probably the easier watch though. It's a little hard to describe succinctly, but it's about this young character, Kino, who travels the world visiting different countries. Each country has a different theme, themes that allow for certain commentary on humanity. There are several great taglines from the show/novels, but probably the most apt one is "The world is not beautiful. Therefore it is".

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