As both a Realtor and Landlord, I see some great suggestions in the previous replies, and would add just a couple more.
#1 If you haven't already, establish some new credit. Something small. For instance, get a credit card and use it - maybe just to charge your gas - then be sure to pay it off each month. But don't run out and buy a new vehicle with a large monthly payment.
#2 The typical security deposit is the same as 1 month's rent. If at all possible, be prepared to offer 2 month's rent for a deposit. We've asked this of some prospective tenants when they've been border-line, and have only been disappointed once. Even then the deposit was enough to cover the damages.