You should get an application with social secutiy number, driver's license number, bank account number, employment information and someone to contact in case of emergency. You should get the name and number of their prior landlord and you should call them and ask for a reference. You should verify employment, ask for a letter or a person to call or a copy of their most recent pay stub. And I always do a full background check including credit check (to be sure they pay their bills on time), an eviction history and a criminal background check. That doesn't mean you should necessarily reject them if they were evicted 20 years ago but at least you can ask for an explanation. Everyone deserves a second chance.
You require that the first month's rent and security deposit are paid in advance and in certified funds, certified checks, money order or cash and I would be careful about cash, best to have a paper trail.
These measures may not protect you 100% from bad tenants, but they will go a long way! Most people with a bad history will run for the hills when you start asking for these things, but good tenants will be happy to provide them.