Here are a couple more options for you. The first I have not used, but seriously considered it when I was evaluating shopping carts for my own business. It is called 1shoppingcart
and I have linked to their list of features. As far as I can tell, even the Starter package has a ton of shipping options.
I use PayPal
myself, but since I do not offer any shipping, I have not used those features. I just checked and it is possible to set up variable shipping rates, but it doesn't look as robust as what 1shoppingcart offers. The one nice thing about PayPal is that their startup fees and overhead are pretty low (lower than most of the services that I compared) so that's nice if you want to get the highest dollar return on the products you offer.
Hope this helps!