When moving from London to LA, we used a US broker, Southern Winds, who took care of booking all the companies for us. We did send sofa, bed and mattress back and a bunch of boxes totaling 250 cubic feet, and that cost $2400, including door to door/packing/unpacking and $20k of insurance. To give you an idea on cost w/o furniture, when we moved to London the year before, same company, 100 cf incl insurance: $1700.
We loved Southern Winds, however we had problems with the company they booked out of the UK, Simpsons Removals - they caused all sorts of damage due to bad packing. But good news is that the insurance works. Maybe if you pack everything yourself it will be better.
Definitely get a few quotes yourself, as cost really depends on where you are shipping to. movingscam.com is a great resource.