I recommend all of these anime and manga because they deeply engaged and entertained me. There are a variety of genres.
...to be honest, there are way too many amazing mangas for me to name them all. The above list is already too long, but I just had to mention these titles. If you want more, go to my "Manga" section in my profile and check my "Reading" and "Read". Anything I've rated 4.5 or 5 stars is something I'd immediately recommend.