This is a good question. Most don't realize, with residential rental properties the management companies and/or landlords are looking for the most qualified tenant and within the shortest vacancy period as possible. That said, you would want to start looking no more than 6 weeks out. Some listings will have a date of occupancy that's much later (which would offer you a larger window of time to secure a property).
Have you located a home or are you still in the market for a rental? If so, feel free to contact me. I would be more than happy to assist you with your search.
Century 21 Diversified