For me, "Good Girl" stands out as Carrie's most complex and ambitious vocal to date. (I know many fans prefer her more stagy, refined, power vocals - which I feel has led to this song being relatively under-rated by some - but I prefer her more raw and Country Blues-influenced voice - and this song would be a must for me). What particularly stands out is her sense of commitment to matching her voice to the spirit of the music, and the number of changes of mood and emphasis she incorporates in this one song - especially the tremendously impressive final section.
Here's an example of a live performance (but several others would also fit)
https://www.youtube.com/watch?v=3d68lyfHmjA
If you're including "Blown Away", I'd put in a plea for the more "stripped down" version she performed in England with a smaller band, before the others crossed the water for the main show,. This was on a BBC chat show on morning TV, and I felt, really captured the mood of the song
https://www.youtube.com/watch?v=JqCFU3Pfm24
I'd also include the Opry performance of "Thank God For Hometowns" - which I think is a good answer to the jibes that she doesn't do "proper Country".
https://www.youtube.com/watch?v=uBjA_vPB-1s
I'd love to include "Forever Changed" - which is a great example of a mood vocal - but you may have to settle for the album track, as Carrie finds it too emotional to perform often.