If you are happy with sending several "parcels" rather than getting a moving company on the job, check out
Pharos Parcel. I used them last year to send a lot of stuff back to Germany for very little money, and their quotes to the US seem rather cheap as well. They have a weight limit, though, so best to call them and check how much you could send in how many parcels.
They use UPS to send the stuff, except they buy freight allowances in bulk and resell them cheaper. That makes it very cheap, but could cause problems should the stuff get lost. Most of the time I believe there is no problem, Yet one of my packages to Germany got lost at first. 30kg arrived all beaten up with only 10kg in it, and UPS trying to get us to sign for it as if nothing ever happened. Given the short time before I was to move to China, locating the remainder and dealing with UPS was a pain, as they kept saying the sender wasn't 'me', but Pharos Parcel, and then having to communicate everything with their office in the UK. In the end it all arrived in time, and Pharos staff were helpful, but still, not an experience I'd like to repeat (next time I'll use thicker boxes!!!) .
Generally, for sending stuff, check weight specifications - one 35 kg package may well cost a fair bit more than getting two 20kg packages (and take significantly longer).
Also, as a general word of advice, pack really, really well and use the thickest boxes you can find. All delivery services expect packages to survive a 1m drop, so if you have 30kg of heavy items (eg books), make sure you use a very stable box or put a few smaller boxes into one bigger one to increase stability.
I try to take one day at a time, but sometimes several days attack me at once.