I am looking for a shipping extension for Magento that will comprehend an item's weight , will figure out if USPS/UPS is the correct shipping method (lowest rate), and will charge add the shipping fee to the cart.
It would be nice if the extension allowed some products to ship with a flat fee, but required others to be calculated.
I can't seem to find this when looking through magento.com extensions.
You can try this Auto Shipping extension. It's not free, but nevertheless is very useful. It will help you to show shipping costs in the shopping cart. You can choose whether the cheapest or the most expensive option is preferable.