Hi Mark,
What you are looking for is an all-in-one online store/shopping cart which works with a third party payment processor. There are plenty payment processors to choose from - there are several threads on these forums that go into more detail about the various options, but Paypal, Worldpay are Nochex are amongst the most popular.
Once you've chosen a payment processor, you need a ecommerce shop system to go with it.
Take a look at oscommerce.com - their system works well with nearly all processors and is a flexible system in general. It's a free all-in-one solution
Ali