As far as pricing goes, as a general rule, the lowest price is not often the best deal, and the highest price is not necessarily equivalent to the best quality of workmanship. Of course, there are always exceptions to generalizations. When checking references, ask about quality of work, fairness of pricing (for the project and change orders), if there were any unexpected delays (and why), and how conscientious the contractor and his or her employees were as far as making the project as comfortable as was practical.
Lastly, one should feel comfortable having the contractor and employees around their house. After all, the crew will be around there quite a bit—and good chemistry can make a complicated and large project feel easy. It is also important to avoid unpleasant conflicts with the contractor. If there are problems, try to remain constructive and find solutions calmly and objectively (as if solving a math problem). If there is a dispute, try to resolve it as quickly as possible to avoid delaying the project.
Remember, both the contractor and homeowner ultimately share the same goal: to have the project go quickly and smooth-ly, and to achieve good results. Careful planning, diligent research, deliberate decisions, and keeping a good professional demeanor throughout the construction process will ensure the best likelihood of a successful and satisfying experience for everyone involved.