I realize this may not be the proper forum, but I didn't know where else to put it.

I created a custom shopping cart a while back where the orders were eMailed to the business owners. The owners would then calculate shipping and taxes, and orders were handled over the phone. They want to upgrade their system to accept credit cards via authorize.net, and want shipping to be automatically calculated.

I don't know the first thing about calculating shipping. Does each item in the inventory database need to have a weight field? And do shipping companies figure in dimensions as well as weight? In your opinions, which is the best shipping company to use?

It depends on the shipping company as to how much the shipping charges are. Some charge by size, some by weight and some by the value of what is being transported. Most do the price by weight, although in set bands, eg 0 - 100g, 101 - 250g ... Speak to the business owners to see which company they use and what they charge at the moment for shipping and handling.