It generally benefits you to dispose unwanted things. Doing so enables you to minimize your packing and transportation needs. In some instances, it's also more practical to sell your furniture and appliances and simply buy new ones when you get to your new home.
 
A moving sale is the best way to do it. Start gathering your unwanted items early and advertise the moving sale early as well. This way you would be able to put all unwanted items for sale. You would also be able to inform more people about the sale. Make the ads big and bright so people will notice them. Strategically position them in areas where more people will see them. Make sure you mention the best items in your sale. Posting online and local newspaper ads would also help attract more people to the sale.
 
However, if you have very expensive items you could instead have auction houses handle the sale. They would be able to sell antiques and other valuable at much higher prices.
 
If your problem is space, you could instead join a flea market. Such venues are already well advertised so all you have to do is show up with your items. Even if you have to pay a fee to join the flea market, it's very worth it. Of course, you can also go online to sell your items too.