I have some slightly different thoughts. My experience is based on 12 company-paid moves in 21 years of marriage, all with 2 kids along, 3 of those moves were overseas. We have used Atlas, Allied, and a few you haven't listed (overseas).

1) I don't think the driver matters much at all. Usually they were contract drivers. The packers matter most, and then the crew chief for loading the truck. If the packing is done right, the driver is irrelevant. If the packing or loading is done wrong, even the best driver won't save your stuff.

2) Go for packing references at the origin. Pick your mover based on those references. If you have a professional moving company the rates differ slightly, for equivalent services. As another poster noted, it is the extras that will kill you. One quote may have them in, another will low-ball it but the extras bring it back to the same price. Unloading is simple compared to packing. Don't pack yourself unless you have done it enough to be good at it. If you do pack yourself, buy proper packing materials. Don't skimp on boxes or paper. Full detailed inventories. Sign off every box when they carry it in to the truck, and carry it off. One set-up box to go in last, and come out first.

3) Have a full and itemized inventory before the packers arrive. We maintain our inventory between moves, it makes it simpler. It is currently over 1000 lines, all with serial numbers, purchase details, reference photos, etc. It makes claims very easy, if you do need to make claims. Household insurance is pretty easy as well.

4) Full value moving insurance. Anything less is a big gamble.

5) Get rid of everything that you really don't need, before the movers give you a quote (or mark it as not going so it isn't priced in). Amazing how much junk we all accumulate.

6) Don't share a truck or container.

7) The packers are your friends. Don't hover over them, but do let them know your expectations. They will usually have one very qualified packer, and some labourers. If you are lucky, it will be a packing team that always works together, and knows lots of packing tricks. If you see things going on that you don't like, stop them and contact the moving company. Ensure that they have plenty of non-alcoholic beverages available. A little extra effort from them makes everything go much easier.

Good luck.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue