You should check with the state - all contracts fall under a state contract law with respect to a requirement of being in writing. Also your state contractor board probably has a set of laws with respect to types of contracts required, especially with homeowners. I know Calif. has VERY strict contract/disclosure requirements when dealing with homeowners that pretty much spell out EVERY detail of the contract, work to be performed, how and when you will get paid (Maximum of 10% down payment).
You should ALWAYS get a minimum down payment - a client who says "I don't pay anything in advance" sounds like someone who doesn't plan on paying anything at all. Also make provisions to get paid as you go. E.G. 10% down, 25% after new service roughed in, 25% after all new outlets installed (2nd level of inspection)...balance upon final. This process of getting paid as you go insures you don't have a lot of money being owed to you at the end.