I am going to present you the most popular manga in my opinion. The best manga are often adapted into anime I will tell you about those of which I think that the manga is better or that the anime or manga is long, so reading is a better option. You can buy these manga in librairy or on internat but you can also find them free on internet,
Genre: Shonen
One Piece is the best-selling in the world and the manga is not finished,
there is 98 volume now with more than 1000 chapter.
The story follows the adventures of Monkey D. Luffy,
a boy whose body gained the properties of rubber after unintentionally eating a Devil Fruit.
With his crew of pirates, named the Straw Hat Pirates,
Luffy explores the Grand Line in search of the world's ultimate treasure known as "One Piece" in order to become the next King of the Pirates.
Genre: Seinen
Death note is finished and there is 12 volumes.
The story follows Light Yagami, a teen genius who discovers a mysterious notebook: the "Death Note",
which belonged to the Shinigami Ryuk, and grants the user the supernatural ability to kill anyone whose name is written in its pages.
Genre: Shonen
Naruto and Naruto Shippuden (which is the naruto sequel) is finished and there is 72 volumes.
It tells the story of Naruto Uzumaki, a young ninja who seeks recognition from his peers and dreams of becoming the Hokage,
the leader of his village. The story is told in two parts – the first set in Naruto's pre-teen years,
and the second in his teens.