Beer - I'd avoid specifying song in the title if you want to encourage instrumental music as well as song. And you might want to consider whether you'd be prepared to tolerate some C&W mixed in with the folk music and old ballads.Louie Roy - "song that tells a story" is one definition of a ballad, but if you're in doubt about ballad as folk song I think you might need to investigate the big ballads handed down over centuries through the oral tradition and which crossed the Atlantic from Britain to the Appalachians in particular (death, sorcery, adultery, incest, fratricide, infanticide, battles, burnings etc) if you're not convinced that a ballad is a folk song. Johnny Collins has a nice story about going out for a drink one Saturday night in Glasgow, and finding that the local idea of entertainment was singing Child ballads round the room.
In the days before Mike Harding's programme, or even before Folk on 2 there was a BBC Radio 2 programme called Country meets Folk. It was fairly eclectic (though prone to renditions of Red velvet steering wheel cover driver-for which see eponymous thread).
Kitty