Get a written estimate from several movers.
The estimate should be based on an actual inspection of your household goods.

Make sure the mover has insurance and is licensed by the proper authority.
For moves from one State to another, a U.S. DOT number is issued by FMCSA. You can double-check a mover's license on www.protectyourmove.gov. For moves within a State, requirements vary. Check with your State, county or local consumer affairs agency or your State attorney general.