When the estimator comes to your house, scrupulously show them EVERYTHING. Draw up a careful list of everything you’ve got, and give them a copy. Particularly point out all your books, which are dense and heavy compared to your other stuff. Don’t leave them any way to say you hid things from them to defraud them.
If you can’t get a “guaranteed estimate”, that is, one which is a binding contract signed by both you and the mover, be very, very wary. Even if you do get one, read it in detail and do not expect everything to go perfectly as described.
Take no flack but be polite, as recommended by Chefguy). Do not accept verbal assurances and do not allow anyone to browbeat you or pull car salesman type tricks on you after the contract has been signed, but treat them like good and intelligent people. Heck, they might be.
Get recommendations from friends.
DEFINITELY check with your local Better Business Bureau for complaints.
Understand that the national companies (Mayflower, Allied, etc.) have local affiliates (Bob’s Moving, Two Men and a Truck, etc.), and check on both thoroughly.
Understand also that your local company will probably subcontract the actual driving to drivers from just about anywhere, and there’s always a risk involved with that – so find out exactly how they intend to cover your loss if their subcontractors make off with your stuff, or roll over on the highway, or get robbed, or whatever.
Unless you have a whole honkin’ huge lot of worldly goods, realize that your stuff will be combined with other people’s stuff on the truck. If you are the first on, you will be the last off. You are unlikely to have any control over when your stuff gets on.
Expect delays, no matter what they tell you or even promise. Two month delays are not uncommon, and longer delays are not unheard of. Plan ahead for them. For instance, if you’ll be going to job interviews anytime in the two months after you arrive, pack a few interview outfits in your suitcase. Pack the essentials for the kitchen unless you can afford restaurants for at least two months. Take camping basics, including comfortable sleeping pads or an air mattress, and something to light up your potentially dark and empty new home.
If you don’t have a laptop, you’ll probably also be without your computer during that time, so scope out stopgaps like internet cafés or the local library, and make portable copies of any files you might need (like your résumé, financial info for the new bank, etc.)
Make sure you will have a valid check, drawn on an account that’s fully up and running in your new location, to hand to the drivers when your stuff arrives. Some of them won’t accept Visa or Mastercard without a 24 hr+ delay, which can mean your stuff goes into storage for a few days, which YOU PAY FOR at high rates. DO NOT accept their verbal assurances that “Oh, of course we take credit cards, no problem!” – get all conditions in writing.
Tell them it’s for your accountant or something if they act like you’re asking for too much in writing, and smile at them. “Oh, my picky accountant, you know how it is, sheesh, so sorry, gotta have everything on paper.”
Oh, and if you do any of the packing yourself, pack much more securely than you might think necessary for, say, UPS. They’re gonna make dense stacks of things and occasionally even the best movers put the dishes on the bottom.
I recommend packing boxes yourself, with Chefguy’s caveat about letting them see inside if possible. Make them lighter than you think they need to be, especially with books. Much better to have two small, managable boxes than one big one.
Your furniture WILL get dings, so if you have heirlooms, insure them at replacement value. Whether your stuff is valuable or not, look carefully at the mover’s contract’s clauses for restoring things to their pre-move state. If restoration is necessary, know that it will be a giant pain in the ass, no matter what.
Get insurance from your regular provider, not just the “add-ons” from the moving company.
WATCH the movers as they load the truck – not because they’re likely to steal things, but because they’re likely to be somewhat more careless if no one’s watching. Be friendly to them and make soft drinks, water, and some basic snacks available to them, and show them where the bathroom is. Tip them afterwards (they’re almost certainly underpaid out of whatever their boss gets off you).
Good luck – I have a truly epic godawful horror story but I hate even thinking about it, three years later.