For a job of almost any size over a few hundred dollars, it is usually important to have a written contract. Here are some factors to consider as you get ready to hire your contractor:
Standard contract terms
Most states have standard contract language that your contractor should be using for a simple contract between you and them. Research online the standard contract language for your state and make sure your contractor is using a standard contract.
Permits
Most municipalities do not require permits for fences, but some do require permits for fences or fences that exceed certain limits. Make sure your contractor knows which permits they will need for the work you need done and then make sure they get any and all permits for your work. Do not let them talk you into skipping the permit step under any circumstances. There will be significant liability for you if you do not get required permits, especially when you decide to sell your house.