Is My Credit Good Enough to Rent a home?

I believe my credit score is below 600. It is due mostly to old collection accounts and charge-offs, like nearly 5 to 6 years ago. I do not have a credit card or any current credit in my name. I have been on my job for at least 3 years and make enough money (at least 3 times the rent they are asking for) to afford the rent. I just dont know if I will be turned down simply because of my credit report. I have been renting from my father (he owns the house) for the past ten years, so needless to say, that rental history isn't on a credit report. I want to move into a bigger home and rent it for now. Will my credit score keep me from moving into a home?