Ok, I've built online stores using both GoDaddy's Quick Shopping Cart and Volusion's product. But is anyone familiar with a good third-party ecommerce / webdesign software package that can then be hosted by anyone? I'm not talking about creating one from scratch using Dreamweaver and ASP.NET (for example), but one that gives all the benefits of templates and shopping cart (with payment gateways) that the products from hosting companies do - except we can customize things how we want and move it from hosting company to hosting company if necessary.
Thanks!

Good question Craig.........
I also want to do this (online store) in the near future and don't know where to start. Hopefully, someone will chime in.

web.com

magento:
 
http://www.magentocommerce.com/download
 
prestashop:
 
http://www.prestashop.com/en/download
 
oscommerce (old but easy):
 
http://www.oscommerce.com/Products
 
wordpress + woocommerce:
 
https://wordpress.org/
http://www.woothemes.com/woocommerce/

Thanks for the options.  I've heard that WebPress' MarketPlace and Jigoshop are better than WooCommerce, but I'm not sure if we'll be going in a WebPress direction yet.
 
I've got some information about Magnento and Prestashop, but haven't really dug into those yet.