Magentocommerce.com
The only main difference between the free and enterprise site is the support (you get none for the free version lol).
They have documents that show you how to skin the cart for your theme. If you are not great at that, you can head over to themeforest.net, type in magento and buy a template.
You can use paypal, authorize.net etc, they have free plugins on their magento connect site for moneybookers, some european payment gateways etc. They have a shitload of free and paid plugins for stuff like custom shipping options, affiliate setup and so on. There is also an option to set up mobile shops but I dont know if you have to pay for that or not.
They ship via usps, ups, fedex, dhl, and you can set up flat rate shipping, table rate shipping, custom shipping, etc.
The first mainstream site I built with it took me a week to skin it myself, figure out the products, shipping, getting it all done. Now I can do it all in a couple of days.
I hear oscommerce and i think its zencart or zencommerce is good as well, but I don't have experience with them.
Here are two examples of layout built on top of magento
http://themeforest.net/item/organic-..._preview/97859
http://themeforest.net/item/furnitur...preview/123693
Best of luck