Time after time when i visit with customers i hear horror stories of how contractors would leave them stranded with half finished projects or they only show up for the first quote and collect a down payment and then vanish into the night with the money never to be seen or heard from again. Sure the insured contractors cost more but like everything in life, you get what you pay for. The reasoning i usually hear from the customer is they chose the uninsured guy because it saved them money or it was somebody's friend and they were able to save money at the same time. I am sure we are all guilty of doing this at least once in our lives. The cheaper price tag lures us in to something we regret. 

If there is one piece of advise I would give my own children if they faced the same situation that brought you to a contractor, it would be this. Take the time to research the company. Access to the world's knowledge has never been easier in this day and age. Look at Facebook reviews, look at google reviews, and look at the company website. Find out if they are accredited or certified, but most importantly make sure they are an insured contractor. The last thing you need when you already are spending probably thousands of dollars on a project is to have something catastrophic happen and there is no way out. You will find yourself staring at an unfinished project and even more problems to deal with. By hiring an insured contractor, you help protect yourself and give yourself an opportunity to recover if things go south between you and your contractor. Researching to find if they are accredited with any major organizations will help you decipher if the contractor is serious or not. Your small time contractors wont have any real accreditation with major companies in their industry.  It takes time and money the smaller companies refuse to put resources to earning that title. Sure it keeps them from ever being able to work major jobs for factories or land developments but when there are plenty of people around willing to pay a contractor without said accreditation AND they have the ability to disappear overnight if they decide the money isn't worth finishing the project then why do it. But as the customer, why subject yourself to such ethic and potentially save yourself 10-15% on a price tag for shoddy product and second hand workmanship. Do the research. Protect yourself and your savings. Choose a company that actually enjoys working for its customers and puts the time in for you to be protected and show you they want to do the work honestly.