Jon,
I've played rarely in public (wasn't good and determined enough), so I can only respond you as a 'consumer'.
As for the repertoire play what you feel comfortable with, the listeners will feel that.
Same advice for the performance itself. There are great storytellers among the British performers, e.g. the McCalmans. If you do not feel comfortable with this style, the audience will feel it. The Corries or Brian McNeill also make you feel comfortable with a bit less of storytelling than the McCalmans. However, their styles would not survive a transplant to a different person.
I love hearing some information to the songs (most solo performers mainly do it for regaining the strength to sing), but I love it with variation (the Irishman Andy Irvine is a good example for that): Tell a personal story to one song (how you found it, why it means something to you, a remotely related story of a friend reminding you of this song), tell its historic background (who fought against whom in that battle; cultural background in 18th century England...), or just tell a single line like 'Now comes a love song, I like it a lot for no particular reason'. People like the variation. Whereas in liner notes, I love to find reliably the same information (Child number, alternative titles, old recordings, background, and all that) to each song, I'd be bored by this in a live performance. Play with your stories, tell different tales to the same song each time and listen to how they react. Listen to other performers when and how they make you laugh or think or be bored by a too long bit of teaching.
I remember one German folk group (Zupfgeigenhansel for those who know them) that made me want to run away by their elaborate information to each song. There was no variation, each time they told their audience the political background and why it was a 'progressive' song and how we should feel about it. It was too much of the same and too much like in school. I came back because I loved their music, but I stopped listening to their tales bwtween the songs.
Listen and experiment, experiment and listen.

All the best to you, but I hope I'll be able to see Martin Carthy at least once before you completely take over his job.

Wolfgang