Personal belongings are important to you, and, as such, it is important to hire a moving team that will do what you expect. Here are questions to ask any company you're seeking to employ:
Do you have any references?
References or a link to online references are very informative, and will help you to form an opinion of how reliable the service will be.
What specific services do you offer?
Moving companies vary in terms of what they're willing to do for you. There are some companies that might refuse to move large items, such as grand pianos, and only provide the lifting and packing of smaller items. Or you might only want a company to do one or two things for you, such as load up a truck you've rented yourself.
Do you offer in-home estimates?
Knowing what needs to be moved is one thing, but understanding the cost of labor to get the job done is another.
Be sure to get everything in writing and secure the departure and arrival dates to avoid any potential hiccups.
What happens if something is damaged?
You've chosen a company you can trust and afford, but what will the company do if they accidentally break something of yours? Be sure to ask what the company's policy is on this subject.