Hire a well known company and get their insurance. Also it wouldn't hurt to video tape the loading.
two things have happened to us. Years ago we moved from one town to another about 60 miles away. They picked up on one day and did not need to deliver for 3 days. The mover while working for a well known moving company was an independent contractor. He took our stuff to his home and used my husband's chain saw. He freely admitted it and even joked that it was dull. We were stunned.
Another time we moved 12 miles so it was done by the hour and cost us over $1200. The two guys stood around and argued how the truck should be loaded etc. taking a ton of time. We complained and were told too bad, that's the bill! It would have helped to have video taped the guys screwing around.