The following list shows the best selling manga which series started in 2014. Actually some of them had already published as magazine articles in 2013, but their vol.1 books were published in 2014. A publications distributor Nippan released this data.
All images are linked to Amazon.
Note: The author is working at destroyed Fukushima 1 nuclear plant (which is called Ichiefu) to clean up the plant, and reporting it.
Katsute Maho Shojo Ha Aku To Tekitai Shiteita (Magical girl and the evil used to have hostile relation)
(redo the life)
Boku No Hero Academia (My Hero Academia)
Tanaka Kun Ha Itsumo Kedaruge (Mr. Tanaka always looks like listless)
Inuyashiki (Mr. Inuyashiki)
One day an old man Mr. Inuyashiki turned into the secret super hero.
Isobe Isobee Monogatari (Story of Mr. Isobe Isobee)
Story of a lazy samurai Mr. Isobe.
Nietzsche Sensei (Mr. Nietzsche)
Story of an eccentric clerk at a convenience store.
Mahou Tsukai No Yome (Bride of the warlock)
The Heroic Legend of Arslan
Source is Asahi shimbun article on Dec 23, 2014.