Personally, I price my rentals in California at the lower end of the price range to give me as much choice of tenants as possible. I have the most interested ones complete an application and then rank them according to a checklist that includes length of former residence (the longer the better), length of employment (also the longer the better), income, references, etc.
Then I finalize negotiations with the top one about the deposit, pets, etc. If all goes well I then ask them to give me payment for a credit check. If there are no major negatives on their report we sign the lease agreement and I accept the deposit. If we cannot agree or they don’t provide the deposit I go to the next person on the list and start the process again.
Once I receive the first month’s rent I hand them the keys and we walk through the property to review its condition. After that, the property is theirs.