If you’re specifically aiming to get better at reading for JLPT, I would recommend focussing on books and not on manga. The reason being that manga mainly consist of spoken language, which has its own difficulties and pitfalls, but I have yet to see spoken language in the JLPT reading section (and even in the listening section, they only use pretty straightforward language).
When it comes to picking books, with N3 grammar under your belt you can basically select anything that’s classified up to Intermediate level in the Master List of Book Clubs, be it an entry in the regular book clubs (Absolute Beginner, Beginner, Intermediate) or one of the miscellaneous books. This doesn’t mean that those books don’t contain higher-level grammar, but they are not extremely hard either.
At the end of many of the book club threads, you can find a satisfaction poll which also captures how hard the participants found that book. There you can get some insights which can inform your choice.
The book club threads are of enormous help because many questions have already been answered, and you can still ask questions even now as many of the participants still watch the threads and are happy to help.
Here are some books that are more on the easier side in my opinion:
- かがみの孤城 (Kagami no Kojou) Book Club - currently ongoing book club, currently in week 6 and taking a break soon, so maybe you can even manage to catch up with the club?
- 狐笛のかなた (Koteki no Kanata) Home Thread
- コンビニ人間 Home Thread (Intermediate Book Club) and コンビニ人間 🍱 Repeat Book Club
- 夜市 (Night Market)
- 魔女の宅急便 (Kiki's Delivery Service) Home Thread - Beginner's Book Club and 魔女の宅急便・Kiki's Delivery Service 🧧 Repeat Club
Happy reading!