J.L.
Be sure to have a few different companies come give you estimates... get references from them and ask how they handle claims should there be any, and also about the insurance they offer. Choose a company with a strong reputation like Atlas, MayFlower, Allied.. please don't use a local company. My husband worked for MayFlower and Atlas for 15+ years so I have learned that there are vast differences between experienced and inexperienced movers.
Good Luck with your big move!!