Assalamualaikum ustaz. What is the best recitation or supplication during circumambulation?
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions and all those who follow his footsteps until the Last Day.
Tawaf is one of the commanded worships and it is a requisite in the worship of hajj and umrah. Allah SWT states:
وَلْيَطَّوَّفُوا بِالْبَيْتِ الْعَتِيقِ
“And perform Tawaf around the ancient House.” 
There are several conditions for tawaf which are:
- Covers the aurah. It is a condition of tawaf the same as the valid condition of prayer.
- Pure from hadas and najis on one’s clothes and place.
- Begins the tawaf from Hajar Aswad. It must include one’s whole body when starting the tawaf at Hajar Aswad. If not, then his tawaf is invalid.
- Must complete 7 rounds. And if one is uncertain then, take the lesser number the same as in prayer.
- The tawaf is performed inside the mosque. And if it is performed outside the mosque, then it is invalid. It is valid if it is performed inside the mosque on the second floor and sutuh (rooftop). And this is the ijma’ of scholars.
- It must be outside the Kaaba, Syazarwandan Hijr Ismail. On the condition that his whole body is outside the area of the Kaaba. 
Regarding the above question, we would like to state that it is sunnah to begin the tawaf with the supplication:
بِسْمِ اللَّهِ، وَاللَّهُ أَكْبَرُ، اللَّهُمَّ إِيمَانًا بِكَ، وَتَصْدِيقًا بِكِتَابِكَ، وَوَفَاءً بِعَهْدِكَ، وَاتِّبَاعًا لِسُنَّةِ نَبِيِّكَ مُحَمَّدٍ – صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ
While in between the two Rukun Yamani and Hajarul Aswad, recite the supplication:
رَبَّنَا آتِنَا فِي الدُّنْيَا حَسَنَةً وَفِي الْآخِرَةِ حَسَنَةً وَقِنَا عَذَابَ النَّارِ
A person can recite any supplication in his tawaf. Reciting al-Quran in tawaf is prioritized compared to non-ma’thur supplication. As for ma’thur supplication, then it is prioritized according to sahih opinion. While the second opinion states that recitation of the Quran is still prioritized. 
Hence, when we are performing our tawaf, avoid talking, selfies, answering a phone call and others. Although it is allowed, tawaf is a worship where we should keep our focus on our worship.