As someone who's only seen the most basic anime shows(NGE/Death

>>158420
Serial Experiments Lain

It's a psychological kinda anime from the late 90's (and it shows)

Your image is from Golden Boy, which is a 90s comedy you might like. Most of the SoL I recommend isn't 90s or 80s unfortunately:
Aria: the Animation
Azumanga Daioh
Barakamon
Beck
Non Non Biyori

Some general recs of essential shows, shows from the 80s/90s marked with *
Baccano!
Bakemonogatari
Birdy the Mighty: Decode
Cowboy Bebop*
Danshi Koukousei no Nichijou
Ghost in the Shell: Stand Alone Complex
Gunbuster*
Hellsing Ultimate
Kino no Tabi
Melancholy of Haruhi Suzumiya
Legend of the Galactic Heroes*
Outlaw Star*
Sayonara Zetsubou Sensei
School Rumble
Serial Experiments Lain*
Tengen Toppa Gurren Lagann
Toradora!
Trigun*
Working!

Movies:
Akira*
Barefoot Gen*
Grave of the Fireflies*
Jin-Roh*
Memories*
Metropolis
Patema Inverted
Porco Rosso*
Steamboy
Tokyo Godfathers

>>158420
80s/90s
>Serial Experiments Lain
>Infinite Ryvius
>Mobile Suit Gundam 0080 War In A Pocket
>space Runaway Ideon
>Memories

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>>158420
watch hajime no ippo/ranma/sailor moon/dbz/db/hokuto no ken for older "must watch classics"

you can watch robotech/gundams/giant robo

try to mix in ovas/movies as you go

>>158455
[spoiler]Ideon is 70s.[/spoiler]

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There are other charts like this on the /a/ wiki. Just keep watching through these until you've finished them all, they're all good in one way or another.

In terms of good 80s-90s classics, then you can just look at the Shonen Jump series that had anime series during that time, I'd especially recommend Hokuto no Ken,Sakigake Otokojuku, Kinnikuman (anime not fully translated yet, only up to 66/67 can't remember) and Yu Yu Hakusho