I have not read the rest of the posts here but Jake is right on in my opinion.
Here is another option for the original OP, don't give a grace period at all. If you have properly screened and set income criteria such that you know people can pay then your tenant will not be late they will pay rent on time or right before!
Second do not trust the credit report. Be sure you check it yourself. I am repeating others but it is important to do this yourself.