Question about taking down payment for applicant

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This is my first time filling an apartment and I am currently going through the screening process.  My question is about down payments.  Do you take them?  At what point do you take them?  If I've already had one application submitted to me with no down payment, and then someone comes along offering a down payment, can I move the second guy to the front of the line?  Should I reject all down payments and process the applications in the order they were received?  Should I only accept a down payment after an application has been approved?  As you can tell, I'm very unclear about how to handle this.  Thanks in advance for your responses!

-Joe