You will find that this varies from Owner to Owner and from Property Management firm to Property Management firm. With this being said, when searching for a Rental, feel free to ask the Owner or the Property Manager what exactly they look for. In my experience, its not just the FICO scores that matter but the overall credit history. When I used to be a Property Manager many years ago, I didn't care what the FICO score was, all I cared about was how were the propective tenants managing their financial affairs. In today's economy, there are many good folks with bad credit or low FICO scores due to loosing a home or a job. To me the important part was not whether or not the prospective tenants lost a home, but rather what have they done since loosing their home? I used to verify employers, references and certainly past Landlords. Of course some people lie, but what is important is that if you are a propective tenant, DO NOT LIE!! I say again, DO NOT LIE!!!! When speaking to references MOM would be the first person to spill the beans, and once a prospective tenant is caught in a lie, its automatically DENY! Tell the Owner or Property Manager what happen, and what you have done to correct it and what you will continue to do. Better yet, document it by writing a letter and attaching it with the application.
Now, I will also say this. Since most of my background is in finance, I will advise you to look into raising that credit score. I DO NOT offer "Pay per Credit Repair Service". All my advise is free. If you would like to discuss, call me at 951-210-2101 and I will advise you FOR FREE on how to raise that FICO score.
Good luck to you!