Who greets first: the one arriving from travel to his family's land, or those who live there? Are there any proofs for this from the Qur'an and Sunnah?

If you are asking about going to greet the one who has arrived, or the one who has arrived going to greet the host, then the scholars have mentioned the desirability of visiting the one who has arrived, embracing him, greeting him, and congratulating him. This is because "it is good to congratulate the traveler upon his arrival, just as it is good to congratulate the sick upon their recovery." This matter is desirable, not obligatory. If the one who has arrived initiates the greeting or contact, it is good and may even be preferable if it fosters unity among hearts.