Should I begin with the "Greeting of the Mosque" prayer, or should I first greet those present and then pray the "Greeting of the Mosque"?

If you enter the mosque and find a Muslim on your way, greet him, because greeting is one of the rights of a Muslim upon another Muslim. If you do not find anyone, then pray two rak'ahs as a greeting to the mosque before you sit down, acting upon the words of the Prophet, peace and blessings be upon him: "When one of you enters the mosque, let him pray two rak'ahs before he sits down."