Definitely try to avoid hiring a moving company if at all possible. The throw out/replace furniture, and shipping boxes to your new place strategy is much less risky if you have a small apartment.
It's just about impossible to find a ethical mover. They charge by weight but you don't get to find out the ACTUAL weight until the truck is loaded. When they come to give you an estimate, it's going to be low so they get the job. Then when everything you own arrives at the destination, they tell you it's an extra $1,000. Either pay or they keep your stuff, and by the way it's an extra $150 per day "storage fee" until you DO pay.
My guess is it would cost around $1,500 to pay a moving company to pack/drive/unpack. If you get one of those "you-pack" deals (they drop off a container which you pack, they pick it up and drive it, you unload it at the other end) you might get it down to around half of that. At least with a you-pack arrangement there can't be any extra charges.