Are you managing the property? Or is the realtor? If the realtor is, they should be able to just ask you the basic questions they need answers to and keep this moving. If you are self-managing, that's a different conversation. You seem very green, I would highly suggest finding a property management company to do this for your while you learn the ropes and how things work.
However, you can also get a copy of "The Book on Managing Rental Properties" by Brandon Turner, and get some really good information.
The main one's to consider are:
Background check - totally clear, or will you allow certain things
Eviction history - totally clear, or will you allow if no evictions for last xx years
Income Requirement - usually 3x the cost of rent
Credit History - totally clear, or will you allow certain things
Pets - yes or no, size, type, number of pets allowed, extra pet deposit/fee
Again, I highly suggest a property manager to assist you with this.
