I am not an attorney, but I have fixed up numerous house and have run 2 construction companies and can speak from my years of experience in California. I would draft my own contract or have my attorney draft the contract or modify the one provided by the contractor to include the following:
Detailed scope of work, start date and completion date with penalties for exceeding the completion date without prior written permission. Also specifying any specific materials, finishes, and any specific objective level of quality of workmanship that you require.
Requirement for providing certificates of insurance including both liability and workers comp (if workers other than the owner are employed) naming you as additional insured. Provisions for dealing with disputes (arbitration or mediation, etc). I would also include provisions covering daily clean-up and protection of materials and contractor's tools, and adhering to all standards of safety as required by OSHA and state and local law.
Total compensation with a provision for written change orders that are approved by you prior to start of change order work. No more than a small initial payment to cover initial materials required for the start of the work to be paid at start of work once all documents (including insurance certs) are submitted. Progress payments to be made upon your inspection and approval, holding out at least 10% until final inspection and approval of any permits, and 30 days after completion or until unconditional lien releases are submitted for all subs and materials for which preliminary 30 day notices have been filed.
In larger time sensitive projects you can also negotiate for of a performance bond which would compensate you for failure to complete the project on time and to the specifications in the contract.
Always check the status of the contractors license with your state contractors licensing agency and verify that the guy signing the contract actually is the contractor whose license is being provided. Also check for any complaints with the BBB or the licensing board.
Check references and never give them any money until all the documents are received and checked out.
Hiring a contractor is serious business and, at least in California, there are protections available to the consumer. It is the consumers' responsibility to learn about those protections and to make sure that you can use those protections to have your job run smoothly and result in a satisfactory result for both you and the contractor. Doing your due diligence when hiring a contractor is as important as when you buy the property. An uninsured worker that gets hurt on your property or a contractor digging up a gas line with a back hoe or disposing of toxic chemicals like paint or solvents into an environmentally sensitive area can result in a huge liability that can easily exceed the value of the property. This may sound like overkill, but in fixing up a property the contractor selected can be even more important than the property. A good contractor can fix almost anything on a bad house, but a bad contractor or a badly written contract can easily turn a good investment into a terrible one.