We used United 3 1/2 years ago when we moved down from Mass.
No complaints, they packed us up and arrived exactly when they said they would. No lost or broken items, move went as smooth as a long distance one can.
Don't know if you have moved a lot (we have) so you may know all this already but I would get a "not too exceed quote" and pay for the insurance. Only trouble with the "not too exceed quote" is I have never seen it "fail to reach the not too exceed price"
, that being said, at least you know your cost upfront.
Good luck