Background Checks Resource

I just bought my first foreclose on the courthouse steps. I have been working on it for the past few months to get it ready to rent out. I have been to Landlord.com for some tips on checking out any potential tenants. Police check seem to be high on the list of priorities. Credit checks seem to be a necessity also. Any advice out there on what to look for?? I do not want to inherit someone else’s problems.