I rewatched the whole of the original Evangelion and the ending movie recently (Netflix doesn’t seem to have the more recent X.0 movies) and it holds up extremely well. There’s some stuff that’s the wrong kind of creepy in that 1990s anime way, but mostly it’s still what it is, just very disturbing on a variety of levels, managing to combine excellent anime fights, great music, an awesomely weird take on certain aspects of the Bible/Judeo-Christianity in general, and a bunch of fucked-up characters, particularly the deeply frustrating lead character, Shinji Ikari, who one I think inevitably spends a lot of time wanting to slap. The other characters on the show obviously feel similarly about him a lot of the time and he’s victim of brutal manipulation as well as being a twat.
If you want a show with some sort of good guy, or characters who seem like good people, you will definitely hate Evangelion.
Trigun is kind of the inverse of Evangelion in a lot of ways, because it trade entirely on the likeability of the characters. All the main characters in Evangelion are basically likeable but kind of, for my money, boring. It’s a show with a lot of visual style and pizzazz and so on, and some good music, but it has nothing to say. All the morals or ideas it comes up with are utterly trite, and it sort of goes around in circles, before coming to a very unsatisfying ending, as @BillButNotBen notes. But it is a fun journey at times. As I recall it also largely avoids being creepy (though I may misrecall, it’s been a while).
It’s not a classic, though, is what I’m saying.
Netflix has several good anime shows - Evangelion, of course, if you’re up for it (it’s a bit like a Harold Pinter or Samuel Beckett play in that it requires a certain embrace of the flaws of humanity to enjoy), Cowboy Bebop is just peerless and wonderful, and you won’t really do better anime-wise. They have the first season of Attack on TItan, which is good, and was kind of a big deal (and is also non-creepy). I’d watch all those before Trigun (though er not Evangelion if you’re not kind of into it by episode 3).
Not Vandelay but despite having the original GitS manga from back in the day, I was unimpressed with both. Both of them exemplify the casual fascism and ultra-brutality that Masamune Shirow often lurches into, without any of the even limited thoughtfulness, humour and humanity Shirow has in his manga. The GitS movie was impressive at the time, but even then it was no equal or Akira or Ghibli. And admittedly I never got past the first season of SAC but that was utterly ghastly, even more “militarized police murder people they’ve labelled as terrorists and don’t for a heartbeat consider that maybe they’re part of a horrifically evil and broken system! Yaaaaay murder!!!” way.
There’s always been this unfortunate strand of “Well they’re ‘terrorists’ so it’s totally okay if we send dubiously-legal death squads to gun them all down!” in manga and anime, which probably has its apex in SAC and The Wolf Brigade or whatever it’s been called these days - the one where Little Red Riding Hod gets mixed up with a bunch of Darth Vader cosplayers with MG42s on gyro mounts hunt and kill ‘terrorists’ armed with handguns and the odd molotov in some weird alt-future where the Nazis won WW2 or something.