Here are some my preferences:

1) Prefer couple with children to couple without.

2) Prefer older couple than younger couple.

3) Very solid credit behavior, i.e., paying most credit cards/bills on time. Bankruptcy or foreclosure may not become issue if their credit history shows good behavior. I place very little attention to the actual credit score. In most cases, credit score means little, credit report a lot.

I can usually find tenants that meet my preference.

My price is always below market. But my standard is very high. That result in most often an event less rental experience. I learned my lessons from my mistakes.