I would teach the "call the framework" sort.
It would be efficient to teach and learn this sort. Students would have a high degree of success and low error rate with implementing this sort.
Edit:
There are a lot of criticizing comments on this answer about the quality of my single sort class. These criticisms are applicable to any answer to this question, which is -
"If you were a programming teacher and you had to choose one sorting algorithm to teach your students which one would it be?"
