List of my favorites: Aoharu x Machinegun Big O Coppelion Cowboy Bebop Death Note [Though I personally only watch just Season 1. I still Own 2 but I didn't enjoy as much] Death Note [Live Action Film] And Death Note the Last Name [Also Live Action] Death Parade .hack//SIGN Hellsing Ultimate Hunter X Hunter [2011] Erased Ranpo Kitan Game of Laplace Fullmetal Alchemist Brotherhood Ghost in the Shell Stand Alone Complex Gurren Lagann Joker Game Kiznaiver Kill la Kill Log Horizon Mushi-Shi Mobile Suit Gundam The 08th MS Team Mobile Suit Gundam 0083 Stardust Memory Mobile Suit Gundam Char's Counterattack Gundam Wind Endless Waltz Paranoia Agent Parasyte: The Maxim Psycho-Pass [Season 2 and the Movie were okay but Season 1 is my favorite] Samurai Troopers [Yes I know in America it was called Ronin Warriors. But the DUB didn't include alot of the context that the Japanese version has.] Samurai X Trust & Betrayal Director's Cut [This is an amazing and tragic origin story of Kenshin.] Rurouni Kenshin [It is disappointing the series never covered one of the arcs of the Manga but it is a solid adaptation.] Samurai X Reflections [Emotions] Space Brothers The Kawai Complex Guide to Manors and Hostel Behavior Tokyo Ghoul [Season 1 only cause 2 was a hot mess] Trigun Wolf's Rain Yu Yu Hakusho Hozuki no Reitetsu Kyousougiga Claymore One Punch Man
The only thing I take issue with is the constraint of Netflix and Crunchyroll. if you use Netflix for strictly anime I would just recommend you quit that and just grab Hulu since their back catalogue on anime is just legendary, but if not oh well.
As for Recommendations
xxxHolic (Comedy / Psychological)
Elfen Lied (Horror / Psychological)
Fuuka (Comedy / Romance)
The World God Only Knows (Comedy / Romance)
as for more, you basically either are watching or have watched everything else I would recommend.
Mob Psycho 100, same creator at One Punch Man. The MC is a nearly all powerful telekinetic who desperately wants to be normal to the point of suppressing his emotions. I personally like if better than OPM.
Drifters, created by Kouta Hirano (Hellsing), At the moment of death Historical figures from throughout time are whisked away by someone to a world. Toyohisa Shimazu wakes up to encounter Oda Nobunaga and Yoichi Suketaka Nasu who decide to free some elves from the tyrannical human government.
Rage of Bahamut: Genesis, the son of a disgraced noble and the son of a thief are caught up in the fight to stop an ancient dragon of destruction from being resurrected and protect a mysterious girl.
I think what you want is Kokoro Connect, covers all the genres you ask for. It looks like the dub is on Netflix, but I'm not sure since I don't have it.
Choo Choo, all aboard the feels train! Your Lie in April, Kousie a piano prodigy can't play after his mother's death but things turn around when he meets Kaori, a violinist, slowly things start to move forward again.
a great complimentary series to that would be,
Ore Monogatari, Takeo looks like a fucking gorilla and his best friend Sunakawa looks like a playboy so poor Takeo never has a chance since girls always fall for his best friend but when Yamato appears he goes for it anyway.
This series is so damn sweet and innocent it is a very funny and uplifting counter to Your Lie in April.