My main requirement is that the tenants named on the lease must earn 4x the rent in gross monthly income (not 3.5x, not 3.9x, not "we paid $100/mo more at our previous place!"). You should also verify employment and rental history from the previous two landlords.
It is also much easier to have a realtor handle the entire process for you. The realtor will list your property, show it, take all phone calls and applications, and will call you when an applicant is fully qualified, has their documentation ready, has ALL of the necessary funds, and is ready to sign a lease. The fee for this service will be some portion of the monthly rent, but it is well worth it.
If you are interested in having a realtor handle this for you, I suggest you call Suzette Teague's office (one of this club's sponsors) at 817-306-1919.