Getting a good tenant, who pays on time and keeps the property decent, is key to having a profitable rental property. Trust me, I've dealt with the opposite, and it is not fun. But how do you weed out bad prospects?
You start with an application, I hope. You can charge an application fee. In fact, I recommend it to weed out those who are not serious about renting from you.
Once you get the application, start by looking at the income. Some people use a standard of three times rent per month. I weed out anyone who has prior evictions, but foreclosures are different. A lot of people walked away from homes when the market collapsed or when their balloon mortgage came due and they could not refinance at that valuation. Those people still have jobs and can pay you rent.
That's one thing to think about. Of course, you don't want to violate the law by illegally discriminating on the basis of race, sex, marital status, etc.
Follow the link to see what else you should be thinking about.