I am looking for an inexpensive, simple shopping cart that will integrate smoothly with my website.
First, take a look at the shopping cart product from the folks at The Right Web Tools. I love their solution because it's the only one I've seen that's full integrated with other online selling/marketing modules and as your website grows all you have to do is flip a switch for additional functionality. Plus it comes with a host of free design, hosting, etc...
You might want to look into Monster Commerce (now owned by Network Solutions) or 1shoppingcart.com . It's been my experience that 1shoppingcart's customer service leaves a lot to be desired and when they do upgrades, they change some feature sets without notifying their customers, however other people swear by them.
If you're the technical type, you might want to try Zen Cart, but you might have the same challenges with upgrading.
I would also caution you about using free or very low-cost solutions; with technology, you certainly get what you pay for.