Here are some suggestion options to configure your shopping cart and charge correct shipping charges to your customers.
This option allows you to set up a flat shipping cost. You can set up domestic and international flat cost something like "Standard Domestic" and "Standard International"
This option allows you to set up shipping cost based on the product weight.
Price Based Rate:
This option allows you to set up shipping cost based on the product price. For example, based on the value of your products, you can waive off shipping cost when a user order value exceeds a certain dollar amount.
Connect directly with USPS or FedEx system:
Some shopping cart has this option which allows you to choose USPS or FedEx API. You have to set up an account with USPS or FedEx and use those credentials to configure this option.