Uh, what part of my advice is incorrect? A contract does not have to be a formal legal document. As long as it outlines the exchange or goods and/or services, details both parties and is agreed and signed by both parties, it is a contract. There is no need to get a lawyer or a document full of legalese. According to my state laws, a signed estimate for work is enough to act as a contract. There is no law that specifies a contract needs to be signed or how said contract is supposed to be laid out.

In my original advice, I suggested the OP write out a full scope of work as well as a detailed description of payment. This is enough to be considered a contract. It can be as vague as "remodel bathroom for time and materials" or as detailed as line item cost for all material.