See this web site for a comparison of various shippers.
Amazon suggest "Super Saver Shipping" which mean - free shipping on $25 orders and more.
Here you can read more Amazon Shopping Tips that will help you save money on Amazon.
One thing that you could try is drop shipping. With drop shipping you do not have to pay anything for shipping and the product provider will ship it right out for you. If you want to learn more about this I recommend that you checkout Worldwide Brands as they are the best in the business and they also have a great learning resource center for drop shipping. Hopefully this helps.
Other people asked questions on various topics, and are still waiting for answer. Would be great if you can take a sec and answer them