This new production of Murakami Teruaki, greatly known for his savage eroticism unrivaled in depictions of high-speed piston-like action and facial expressions accompanying orgasm, is, of all things, in the genre of "Younger Sister Moe"!

What are some classic animes that an anime lover should definitely watch?

There’s no anime “Everyone must watch”. However, I can recommend some stuff that rarely pops up in recommendations. Here’s some stuff from my “watched” list that is REALLY hard to accidentally bump into. Magic Knight Rayearth 3 girls thrown into another world.
I admit that I only watched first season, and for some reason lost interest in the second one.
But … it is surprisingly well done. Seikai no Monshou This anime has some of the best world-building.
It is about distant future and space elves.
Beautifully done, although it is rather short (13 episodes). RahXephon Has one of the best mindscrew segments.
Evangelion level material. Devilman Lady This is one of the examples when a director took source material by Go Nagai….
and turned into pretty much a gothic horror level material. Watched it with Jaw Dropped.
Absolutely amazing stuff, especially if you saw the source material which on occasion almost looks silly (due to drawing style). Cutey Honey Shin Cutey Honey Original cutey honey was shot in 1973 (nineteen seventy three, yes), and is completely unlike any anime you would see today. It has one of the catchies opening I’ve ever heard.
(with incredibly silly text, if you can udnerstand at least half of it) However, it is quite silly and childish, until there’s suddenly on-screen dismemberment, that is. It is quite formulaic, and silly… but…. If you sit through the 1973 material and then jump to shin cutie honey (1990s), you’ll be treated to surprisingly amazing animation and one of the best opening reimagining. Just take a look at this: And then: That was quite amazing.
Now… And here’s link dump for high quality stuff that is rarely being mentioned nowadays: Shihaisha no Tasogare Ibara no Ou Kemonozume Samurai Champloo Pale Cocoon Ajin (only for the first season.
2nd one was bad) Sidonia no Kishi Black Magic M-66 NieA Under 7 Kure-nai Seirei no Moribito Natsume Yuujinchou Mushishi Kyougoku Natsuhiko: Kousetsu Hyaku Monogatari Kurenai no Buta Serial Experiments Lain Kidou Keisatsu Patlabor Kidou Keisatsu Patlabor: New OVA Haibane Renmei Tenchi Muyou! Texhnolyze Fruits Basket Bishoujo Senshi Sailor Moon Trigun (Yes THAT trigun.
Do you remember when somebody last talked about Trigun? I don’t). School Rumble Akira Ghost in the Shell Neon Genesis Evangelion Azumanga Daioh Mononoke Hime Great Teacher Onizuka Planetes Majo no Takkyuubin Slayers Tenchi Muyou! Ryououki Urusei Yatsura Hayate no Gotoku! Ookami to Koushinryou Mnemosyne: Mnemosyne no Musume-tachi Ga-Rei: Zero That would be most of them. Go through the list, check each page, and see if any one of them catches your interest.
This stuff is in general quite good. Now, how much free time do you have, again?