We don't have a required time-line in Virginia. I define an expectation in my ads to avoid getting hounded with status questions. We tell prospects that applicants will be processed within 2 business days of the application being complete. I disagree with @Richard F. on the premise that applications must be processed on a first in basis. As long as you are making your decision based on what applicant best meets your criteria, and not on any protected class factors, you have every right to choose the candidate that you feel has the best likelihood of meeting your lease terms. I even do highest and best with rentals, like we do with sales, if I have more than on acceptable applicant. We just let them know that we have multiple applicants and ask them what is their best offer of rent amount and lease term. We have gotten as much as $300 more than ask price with this process.
Your risk if sitting on applications is that the good ones will move on to another property and you will lose them. Only desperate candidates will let the application sit pending a decision for a long time.