Congratulations on becoming a Landlord! I hope you do your homework and be sure not to violate any Federal or State Fair housing Laws. Here are just a few things to remember:
Never asking anything that could be interpreted as discrimination -- which would include any questions about: race, color, religion, sex, national origin, disability, familial status, whether someone is married divorced, gay, and you can't even ask if someone's ever been arrested!
You CAN ask: why are they moving? When do you plan on moving in? What is your monthly income? Will you have the security deposit and first month's rent available upon move-in? How many people will be living in the apartment? Can you provide references from your employer and former landlord?
References from an employer can give you a sense if they have stable income, and if you can speak to a former landlord you may learn if they are a difficult tenant. You can ask if they have ever been evicted.
You can also ask if they have any pets -- if you have a no-pet policy you want to know right away and establish that fact. Also ask if THEY have any questions!
You would also want to run a credit check on them for your own protection.