Steven Zahm@ David
Categories do support the hierarchical structure required for this. They also support an unlimited number of children categories. You would add your four parent categories and then add as many children categories as you wish. Each child category can also have its own children. Technically there is no limit to the child category depth although practically it really does not make sense to have more than a few levels deep.
To filter by these categories, you would need a template which filters by category such as cMap. Any of the templates, which is most of them, which has a category drop down will do. Now, if you want multiple category search, like this site employs that would require custom development, a service which I do provide.
Hope that helps, let me know.