Personally, I became a fan of Chameleon Circuit before I knew what Doctor Who was, and find the variety and style of songs pleasing. It's not something that appeals to everyone however, and after I became a whovian, the enjoyment of the songs improved greatly. I would show Chameleon Circuit to most Doctor Who fans, and unless your friends are nerdy, not too many other people, because the lyrics to every song but "Teenage Rebel" are not easily mistaken for anything other than a doctor who themed song. Over all, I would check it out, especially for you whovians.
(PS- It sort of counts as fanfic, right?)