Do not hire a contractor on price alone. Some remodelers with the low prices will continually ask you for money to finish the project. The price difference in quotes is usually due to the quality of materials used, quality of craftsmanship, and warranties offered.
Make sure the company you are looking to hire is easy to get a hold of. The last thing you want is a half-finished kitchen and a vanishing contractor.
Get everything in writing, including the types of materials that are going to be used and any sort of warranties or guarantees.
Ask for current references and see how long it takes the contractor to get you this information. If they are proud of their work, they should have a list readily available.
Do not pay a major portion of the money up front. A down payment is fine, but paying in full before you have any work done is a recipe for disaster. It is a good idea to set up a payment schedule based on the work finished.