There are so many settings of many of the Child ballads, it's not so much a case of choosing the right ones as choosing the right tune and arrangement. Presumably you're talking about you (or someone else) singing them not just doing an instrumental version?
In which case I'd say just keep experimenting until it sounds right. Some songs probably just won't work for you, while others will. Rather than play the tune, which could detract from the singing rather than supporting it, if you experiment with chords to give a sort of reedy drone in the background, that might work. It's worth trying left-hand chord buttons without the fundamentals (and possibly with 5ths removed) for that sort of effect. You don't want too fussy an arrangement, as it's all about the story really, but if you want to do something fancy it might be better in between verses as an instrumental interlude at some point.
Oh yes, and there's the issue of the key. Being a "GFC man" you have a good choice of keys there, but do make sure you've got a comfortable singing key for the voice in each chosen song.