Content appearing under specific tabs
A multi-level taxonomy could accomplish this for you. Something like:


Music


Rock
Classical
Jazz

Politics
News


National
International
Sport



Create this, and then add a field for it on your single content type. Then use the Taxonomy Menu module to create a menu from your taxonomy, and the Menu Block module to place both a top level navigation, and the sidebar navigation. You can adjust what level the menu starts at for this. 

Your taxonomy menu will link to each taxonomy term listing page, which is a default view. Further, if you setup URL aliases for your taxonomy, and then rebuild links, each page will have a meaningful URL (home/news/international). You can take it a step further by adding URL aliases for your content type as well, and use the taxonomy term path in that so you end up with (home/news/international/title-of-article).