What is prescribed for the worshiper to say after the opening takbir in both audible and silent prayers, and what is the wisdom behind that?

The opening supplication (Du'a al-Istiftah) is a Sunnah (definition) for every worshipper, whether an Imam, a follower, or praying alone, in both audible and silent prayers. As for seeking refuge (Istiadha), it is legislated for whoever intends to recite the Qur’an, based on His (the Almighty's) saying: [So when you recite the Qur’an, seek refuge with Allah from Shaitan, the expelled]. And whoever does not recite should not seek refuge. As for the Basmala, it is legislated for whoever recites Al-Fatiha and the beginnings of Surahs, and one is given a choice regarding it when reciting the middle parts of Surahs. The preponderant opinion is the obligation for the follower to recite Al-Fatiha in both silent and audible prayers if they do not hear the Imam's recitation, and it is a pillar for the Imam and the one praying alone.