Moving is expensive, good movers aren't cheap, cheap movers aren't good, you are the shipper, the movers are the carriers. It goes by weight if going distance so try to be exact on description of items to be moved over the phone so to get a good estimate, if you tell them one thing and it's another, they'll want you to pay for it even doing it through uship. Try to have some moving company estimator's come by and look at it, it's free, ask about guarantees, ask to see the weight ticket so you know what your paying for. I know you have a few movers in your area. Make sure it's packed well if someone else is handling it. I've been a mover nearly 30 yrs and been in your area hundreds of times, you have the resources there. Consider renting a trailer if you can pull it? If it's junk and you don't need it, toss it, don't pay someone to move it!
Like I said, moving isn't cheap and you get what you pay for. Hope it helps, good luck.
p.s. Don't call me, I'm getting out of the business.