How long would be a reasonable time to forgive a potential renter's prior history?

Due to the housing market, my house flipping is turning into rental properties. How much time should pass before forgiving non-felony criminal history? Cannabis possession, domestic violence, vicious dog, etc. Can I legally refuse anyone with charges greater than traffic offenses?
Being a corrections officer, I know the rate of recidivism. I’m afraid I’ll never rent to anyone!