All moving companies are required to carry cargo insurance. Please be aware that this is different than furniture liability!
When comparing local quotes, having the proper amount of men for your move is very important. Many people think that 2 men are adequate to move your home. Unless it is a small move, you might want to add additional men. You might pay a higher hourly rate, but will save in the long run with only being billed a fraction of the hours. Having more men will also eliminate the fatigue of the movers to ensure that all items are handled as they should be.