If you are starting from scratch, you should create a web application. This site does an excellent job of explaining the differences, but the main difference is that web applictions will compile down to a set of DLLs that can be deployed to your server. The site is built as a unit, and has much better compile time error detection, as well as better intellisense. Web sites are a loose collection of pages that Visual Studio does not considered to be a unit.
Web sites are available in Visual Studio for backward compatibility, and can be used if you are maintaining an old ASP Classic site.