Priority Of Picking Tenant?

Hi, all, first-time landlord having a question of picking tenants.

I received two very good applications (decent income, excellent credit). They choose to rent because of relocation for job. What priority should i consider in picking one? First come first serve? May i decide on anyone i prefer even though background checking process already started on one?

One family can move in immediately, no other demand.

The other moves in a week later, asking $100 off rent (which is $1900), and an option to extend lease for a second year. They also will throw away my new carpet and replace with laminate at their own cost.

Any suggestion appreciated.