It is from the sunna to recite some chapters (surahs) of the Qur’an daily. You should strive to introduce these into your routine gradually, and ideally memorize them completely.
 Surah al-Sajdah (32): Jabir ibn `Abdullah said that, “The Messenger of Allah (Allah bless him and give him peace) would not sleep until he recited Alif Lam Mim Tanzil al-Sajdah and Tabarak Alladhi bi Yadihi al-Mulk.” [Tirmidhi]
Surah Yasin (36): Jabir ibn Samura related that “The Messenger of Allah (Allah bless him and give him peace) used to recite Surah Yasin in the morning.” [Tabarani] This is an authentic narration as Haytami clarifies in his Majma` al-Zawa’id.
 Surah al-Mulk (67): Abu Huraira said, “I heard the Messenger of Allah (Allah bless him and give him peace) saying, ‘There is a Surah in the Qur’an which contains thirty Ayat which will keep interceding for a man until his sins are forgiven. This Surah is: Blessed is He in Whose Hand is the dominion. (al-Mulk).’” [Tirmidhi]
General Encouragements and Performing a Regular Khatm
Other encouragements made by scholars are often specific applications of the general virtue of reciting the Qur’an, and can sometimes be based upon weaker reports indicating a virtue found in its recitation. However, it is more virtuous to have a regular completion (khatm) of the whole Qur’an, as well as keeping up with the daily recitations mentioned above.
Nawawi relates in his Adhkar that it is authentically established that the early Muslims would gather at the completion of the recital of the Qur’an saying, ‘mercy is descending.’
The Messenger of Allah (Allah bless him and give him peace) is reported to have said, “Whosoever prays an obligatory prayer, has an accepted supplication. And whosoever completes a reading of the Quran, has an accepted supplication.” [Tabarani, al-Mu`jam al-Kabir]
Darimi authentically relates that Mujahid, an Imam in the Qur’anic sciences amongst the Followers of the Companions, once sent for someone, and when they arrived, he told them, “I only called you because we wanted to complete a reading of the Qur’an, and it has reached us that the supplication is accepted after a completed reading of the Quran.” Then he said, “So supplicate, all of you, with [many] supplications.” [Darimi, al-Sunan]
It is also of the proper manners upon completing a recital of the Qur’an to begin another recital immediately through recitation of the Fatiha and the opening verses of al-Baqara. Nawawi notes that this is a recommended practice as the early righteous loved this. [Nawawi, al-Adhkar]