I'm glad you asked
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Since you seem like a beginner, I recommend starting slow, so watch some normie animes first. I recommend watching: Mirai Nikki, Attack on Titan, Sword Art Online, The Promised Neverland, One Punch Man (I liked both seasons, but the second one lacks animations quality compared to the first, still pretty good story and since the manga and webcomic are still going, we will eventually get more seasons. I totally recommend the manga too btw), My Hero Academia (at least the first two seasons and the first half of the third one. Maybe the first half of the 4th one as well). All of this are relative short shows that are aimed to a general non-anime watcher audience, so it should be enjoyable, even for you Mr. Normie.
Now, on to the good stuff, after having some training with the ones above, I recommend going trough this ones: Death note (is a classic and for a reason). If you liked Death Note you're probably gonna also enjoy Code Geass, is not exactly like Death Note, but both have smartass main characters trying to outsmart opponents, so if you're into that, you'll love those two. Next I recommend Psycho Pass (at least the first season, I haven't even watched the second one), Steains;Gate (both seasons I recommend, but even more I recommend playing the visual novels, you can get them on Steam for fairly cheap), Clannad (if you like emotional shows and crying, the first season may be a bit slow, but is totally worth the wait. Also has a visual novel you can buy on Steam and I recommend it because it helps understand the ending a lot more), and finally I recommend watching Hellsing. You'll find that Hellsing has two versions, I recommend watching both, but first watch the original and then watch the OVAs.
Now that you're a veteran weeb, you need to step up your game and watch some classics so that you can be part of the meaningful conversations. First I recommend watching Hunter x Hunter, is a very good story that in theory is still going in the manga but we will probably never get a continuation on the anime, at least not any time soon. It has two versions, I recommend watching the 2011 one. I also recommend you watch the Monogatari series, is a very confusing show in terms of how to watch it, since they're so many season and what not, but just Google it and decide whether you wanna watch the episodes chronologically or in the order they first aired. Also watch The melancholy of Haruhi Suzumiya. Just like Monogatari, the episodes didn't come out in order, so you have to decide the same thing. Good luck getting through the endless eight arc, hahaha. Now that you have watched all of this, and preferably more, then and only then you can be worthy of watching Serial Experiments Lain. That is all I got for today.
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