Be sure to ask around for recommendations, and check with your local Better Business Bureau office to see if any complaints have been registered about them. Ideally, you should check out both the national company as well as the local agent. The moving agent will send someone over to your home to review the contents of your home and provide you with an estimate based on this visit. If you are getting rid of a lot of things, be sure to tell the estimator what is or is not being moved. Local movers generally charge by the hour.
Interstate companies charge by the pound.
These are costs that are charged by the hauler and can only be negotiated with their approval. These, along with packing charges and materials charges need to be included when comparing estimates. The estimates you get may be quite different depending on how much weight the estimator thinks you have. Don't necessarily go with the lowest weight estimate, you'll still be charged for actual weight and mileage charges in the end. One good idea is to take the highest weight estimate and have the other two movers revise their estimates based on this weight.