#1. Mairimashita! Iruma-kun! - You may've seen stills of the anime and been turned off by the weird, perhaps cheap art, but this is actually really good, and it's the only non-romcom I've been reading consistently for the last few years. It's like early-entry Harry Potter that doesn't get too dark, while still being serious and fresh enough to be entertaining for the adult reader.
Plus, it'll last you a heck of a long time, with 377 chapters. Don't be intimidated by this, and remember that you're free to drop any manga you find boring. But my guess is you won't be bored.
#2. Takarakuji de 40-Oku Atattandakedo Isekai ni Ijuu Suru - This is about a random dude who won the lottery in Japan, found a portal to an isekai world that he can cross into and leave at any time, and he spends his fortune helping this primitive civilization develop itself. Like, at one point he's teaching the Medieval princess how to fill out spreadsheets on Excel, though for the most part he helps them gradually move up the tech tree by their own efforts. My only warning is that the English translation basically stops around Chapter 66, leaving this story incomplete.
#3. Melancholy of Haruhi Suzumiya - I discovered this one a few months ago, and it was weird and amazing. It did the Kara no Kyoukai "broadcast out of order" thing about a year before Panoramic View came out, and it did it well. My only regret is the lack of new content after the movie. Watch the anime for this one, and do not skip the "Endless Eight".
In a nutshell, this eccentric chick is God and doesn't consciously realize it, so aliens, time travelers, and psychics from across the universe have converged on her location to quietly monitor her and keep her from destroying/remaking the universe on an unconscious whim.
#4. Kanojo mo Kanojo - A trashy romcom but one that's fun and clever. Read the manga, not the anime.
#5. Milgram - An anime music video series that you can find on YouTube. There's a group of 10 "prisoners". Each sings a total of 3 songs, hinting at the murder they committed.
#6. Fire Emblem: Genealogy of the Holy War - A video game released for the Super Nintendo in 1996. An old-school Japanese RPG with incredibly deep lore, albeit constrained by the low memory and storage of the SNES.
You can play it online by downloading a SNES emulator, such as Snes9x, and then a ROM for this game with an English translation patch. Trust me, I'm a complete blathering idiot with zero computer literacy skills but I figured it out by myself in one evening, and you can too. I played it on a laptop, but reportedly you can set it up on mobile if that's more up your alley.
The game took me about 2 months to finish (I mainly played it at night), and then it had a 99 chapter manga by Mitsuki Oosawa, which is a deep dive into the events of the game. The manga does get a little freaky at times, as it's done in the style of a 1990s shoujo and the game itself does have some weird plot points which the manga heavily emphasizes, but if you can stomach that, then it's a pretty good read up until the end of the game's first act (c. Chapter 60). The chapters are pretty long, so don't let the whole "60 chapters" bit fool you. This will take you a little while.
#7. Silver Plan to Redo from JK - A story about a woman who wasted her life, and entered her 50s in a state of homelessness. She dies and reverts to her teenage self, back when her family was still rich (the 1990s economic crash bankrupted them). Her original self was a heartless spoiled brat but she resolves to be better and live frugally. Basically a real-world take on "reformed villainess" storylines. I enjoyed this manga quite a bit, and it hasn't ended yet.
#8. No, Miyahara, Not You - An innocent fluff-piece about some kids. An enjoyable read, though there's not a lot of chapters.
#9. Ascendance of a Bookworm - Just try it. It was different and fun.