The trouble with picking standards which have been sung unaccompanied by people like Anne Briggs is that it is very hard to perform a version which bears comparison. Even very good professionals like Cara Dillon have failed to pull it off on occasion.

Pick songs which are well known but which she can interpret herself, or put her own stamp on them. You are in New Zealand, try Farewell to the Gold, or others by Paul Metsers.

How Can I keep from Singing is a good suggestion, and its pretty traditional in that nobody knows who wrote the words (though Lowry clearly did write the melody). Just don't listen to Enya, unless its to hear how not to do it.