It is important for every Muslim to concern himself with the Quran. 
However in the month of Ramadhaan it would be even better and it is even more important to recite it. 
Allah revealed the Quran in the month of Ramadhaan and the messenger of Allah would strive hard to recite the Quran and perform righteous actions.
The Prophet  (صلى الله عليه وسلم) recited the Quran with Jibril in this month. So we know it carries great virtue - and the Muslim should give it its time.