The best way to weed out a lot of potential bad clients is how you screen them. Fisrt, have an application fee. this should be the cost of running a background check (sheriff's dept.) and a credit check. Then have stipulations on the rental agreement i.e. no pets allowed...no more than 'x' number adults can live in the house. Income of tenants must be above 'xxx' per year, etc...
Then you can hire a property manager. the avg. cost is usually 10 percent of the rent. they handle all the calls, and dealings with the tenants. the managers only call you when property damage exceeds a threshold that you've set for notification. for instance, you tell the manager to call you when damage exceeds $50 dollars.
There are all kinds of stipulations you can put in a rental contract, just be mindful of discrimination laws.., you can't say things like no more tha 3 children, or something like that...check this with the state the house is located in. Check the age of the house as well, if it's older than 1976, you'll have to disclose lead based paint.
Good luck.