We have moved many. many times, and whether a move was good, bad or indifferent, one thing I would say is never take your eyes off the packers for a minute. For them it all pays the same, but their random carelessness can cost you a priceless heirloom.
They don’t get paid all that well, so they sometimes have sticky fingers (as in the time they broke open our piggy banks, took our Christmas money, and then neatly wrapped the broken banks up and packed them).
Movers are also not necessarily the brightest folks so sometimes you need to make sure they don’t do something really dumb (like the time they turned my mother’s drop leaf dining table upside down, loaded it with boxes of books and were about to swing it off the end of the tailgate when my mom caught them).
And sometimes they are tired and moving essentially by remote control, as in the time they packed my grandmother’s sandwich and the typewriter she was using to type a letter to the landlord, with the half-finished letter still in it.
When you ask for the bid show the rep everything you plan to move, absolutely everything, so they can make an accurate bid that includes all the packing materials.
Otherwise, as others have said make sure you follow your employer’s rules, get everything in writing, check with folks you know who have moved for their recommendations, and really do check everything off the various lists at both ends. Also. follow the truck to both the empty weigh in and the full weigh in and document the weights.
And here’s a big one: if they don’t pack it themselves, they will not cover any loss or breakage. So your stuff that is still in boxes can be moved as is, but it will not be covered by insurance.
Personally, if I never move again I won’t mind at all.