i once rent to some one who make the house really dirty when move out. But when I send an over $4000 bill to him, he send me a check in one week.
So I do not care if the house is possible be demaged, but the tenant can take responsibility. The credit and income are most important items to reflect the tenant ability of resposibility.
Check credit, inome, rental history to make decision.
Many tenants have multi-children can be good tenant.