Moving yourself might make more sense for the short, across town move but you should consider professionals for longer moves. This appears expensive at first but here are two ways you can find affordable moving companies that can meet your needs. 

The best way to make your move cheaper is to locate a company that is moving several families to the area you are moving too, by doing this they can offer cheaper rates since you are all moving to the same location. Independent moving companies, not the big name companies, do this often and offer the same level of service as the big name companies. Call different companies to see where their truck are going. 

Another way to save money is to check with companies that primarily move businesses. Though they are focused on businesses they might have extra space on trucks where they can place your furniture. This will require more research on your part but it could prove to be very economical.