Shopping carts should control the inventory / shipping charges. Depending on your level of knowledge, most carts can be skinned to almost any layout - some easier than others.

As far as Paypal, there are a few options depending on where the merchant is located. They offer the IPSP (Internet Payment Service Provider) or 3PP (third party processor). And they offer an electronic payment gateway (Payflow) which would require a merchant account as well.

How Does a Credit Card Transaction Get Processed might help explain a bit more.

Some more electronic payment gateways that you probably have heard of are LinkPoint / YourPay, Authorize.net / Cybersource, and Protx. 2CO is another example of an IPSP (but their business model is a bit different to help circumvent the card associations regulations).

If the merchant is in the United States, there are hundreds of possibilities for them and thousands of ways to get those possibilities.

CandyPress and Comersus are ASP / .NET versions if you are familiar with that code. Comersus was fairly easy to skin a couple of years ago. There is also an ASP cart from Metalinks.com that is really easy to skin and comes with some basic options.