A moving company should provide you with a contract. If they do not, ask for one. Here's why. You will want to insure all of your items are protected from problems like theft and damage. If they do something that causes your items to be ruined, then having a contract can help you to get them back. In addition, have your attorney look it over quickly to insure it is valid.
Most moving companies will have experience. If you are working with a new company, this does not have to be a bad thing, unless you do not do your homework. To know if a new company is worth working for, talk to them about their experience, their insurance and how they will protect your items.