If you want to see if a person would make a good employee, see if they were previously a good employee. Call their previous employers. If they are young students and perhaps have never had a job, ask them to provide report cards and a list of their teachers/coaches as references. They need not be strait A students, but everyone should be able to pull off a 3.0 even half asleep.
Everyone makes mistakes in life, including criminal, financial, or personal, but it's the patterns of behavior that are most indicative of future behavior.
Here's a tip though, don't rely too much on the interview. A person's charisma, personality, and charm say very little about how responsible and hardworking someone is. I'd even venture to say that a person's charm only makes it easier for them to get away with being dishonest.
As far as the background checks... they are costly and don't truly indicate whether a person will be an asset or not to the company. But to cover your *** against major liability should the person be a sex criminal (easy to find out if they are a registered sex offender), or perhaps a violent criminal, you could tell them during the interview that you will be conducting a background check and would like to know if there is anything they would like to tell you beforehand (such as warrants, arrests, or convictions).
My supervisor got written up for hiring someone who was flagged by the background check. Wasn't really his fault because accounting (who does runs the bg checks) told him "it's probably just a traffic ticket". Anyway it turned to out be a sex crime! Well, kind of.... apparently peeing in public counts as a sex crime. But this just goes to tell that a BG check might not tell the full story. Hell, I can't even count the number of times I've pee'd in public.