How and where to get tenant's credit report and other Qs

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Which sort of resource do you guys/gals use to look up your tenant's credit score, rental histories, and past crimes/evictions? 

Also, any other things you've learned to screen for in your experiences? Any tips on finding "the best!" tenant? Any big red flags you've noticed pop up with people over and over? 

Last question, is the application fee typically supposed to cover the credit checks?