Agree with screening but not on lease. My lesson learned from years ago - I had a guy and girlfriend both on the lease. They started fighting, calling the police and me about weekly. The police called me to ask who should be removed. It was messy. Now I put the most responsible adult on the agreement, usually the female as I've found them to be the more responsible.
Agree on all adults on the lease. I would also make tenants find a guarantor who will sign a guarantor form, if possible. It could be a relative that lives in the same area that has a good job. A former tenant of mine wanted to end the lease early. I called the guarantor who helped find a mutually acceptable solution.