First make sure they are licensed, bonded, and insured. Next I would see if they are a good fit with you. By that I mean Do they do 300k Kitchens? or do they do 12k Kitchens? Which are you looking for? Next you may ask for some RECENT references. How ever many would cure your curiosity. Then actually follow up, ask about the work quality, how many (if any) change orders those customers got hit with, was the contractor there when they said they would be there?, was there good communication? Was the contractor over extended on his labor? Is he doing all the work himself? Check up on him to see if he actually has a current license (in wa state thats easy look up online). Last thing to mind is talk with him, meet with him (or her). Are they pushy? Can you see yourself dealing with this person for the next XXXX days?
Those are things that come to mind.... there are about a million others.... so post follow up questions if you like. Hope this helps