As the property owner, you probably do not want to rent to just anyone that walks through the door. You want renters who are going to take care of your units and condominiums as if they were their own. This is always a difficult challenge, even in the best of circumstances, but a reputable property manager will know the tricks of the trade.
As the landlord and property owner, you have a significant amount of influence in determining the individual qualifying and screening factors. This will depend on a number of issues, such as the property neighborhood, state of the local economy, and other issues, but these processes should be clearly defined before you sign a contract with any property management firm. Owners usually do not want to intervene in this process once the company has been hired. This can lead to issues of fair housing and discrimination lawsuits.
The final contract that is signed by both parties is going to be the sole, legal document that binds the two of you together. Ask for a copy of their standard management agreement in advance and review it thoroughly. Make your own notes and suggestions in the margins, and always be sure to ask for references and visit their other properties before you sign on the dotted line.