Upon entering the Prophet's Mosque, is it more befitting to pray the two rak'ahs of "Tahiyyat al-Masjid" (greeting the mosque) or to visit the Prophet, peace and blessings be upon him, and greet him, and what is the preponderant opinion regarding this?

The Prophet's Mosque, like other mosques, falls under the ruling of Tahiyyat al-Masjid (greeting the mosque prayer). The Sunnah is to begin by praying two rak'ahs as a greeting to the mosque, and then to send greetings of peace upon the Messenger of Allah, peace and blessings be upon him, for whoever wishes to do so. The grave of the Prophet, peace and blessings be upon him, was buried in the chamber of 'Aisha, may Allah be pleased with her, which was outside the mosque, and the presence of the grave within the mosque was not intended for its own sake.