In terms of your concerns Kim has some good ideas. What you require is to tell the Landlord before he runs your credit and to also inform him to contact the previous landlord for proof you didn't miss any rental payments. Most home rentals only require a minimum of 30 days notice. Provided you have enough income and make the 3 to 3.5 times requirement you should be able to find a place. If you want any help feel free to contact me.
Keller WIlliams Realty