Is the Basmala prescribed before reciting what is readily available from the Qur'an after the Fatiha in prayer?

The first (and best) approach regarding the recitation of what is easy from the Qur’an after Surah Al-Fatihah in prayer is for the worshiper to recite the Basmalah silently if he is reciting from the beginning of a Surah. If he is not reciting from its beginning, then he has the choice. Indeed, Ahmad (may Allah have mercy on him) recommended reciting the Basmalah at the beginning of every Surah, both within and outside of prayer.