I'm not alternative myself, or teenybopper. If it looks good, I wear it. Simple, eh?
I'd recommend getting 'International Superhits'. All the well-known songs, all fab of course, and after you've fallen in love with that, you can start with 'Dookie', 'Warning', 'Insomniac' (appropriate), 'Nimrod', and 'Shenanigans'...they also have two before-they-were-famous albums, re-released to capitalize on their success, but we'll worry about those later. Ready...GO!