Watch Redline, Demon City Shinjuku, Ergo Proxy, Psycho Pass, GITS series (not the netflix animated crap), Berserk, Ninja Scroll, Jormungandr, Black Lagoon.
Ergo Proxy I just didn't get.
Psycho Pass I really enjoyed; good depth of story and exploration of the pros and cons.
GitS series is probably my favourite anime, and very high up in my favourite anything.
Berserk is good, and descends into Evangelion-level insanity as it progresses.
Ninja Scroll is forever a classic. Worth a re-watch every 5-10 years. I'm due.
People really are ungrateful and deserve the borderline idiotic Attack of the Titans rather than these classics.