I would advise both Selection and Merge Sort on the general sorting algorithms. Both are relatively straight forward compared to their friends. But if you can only teach one and the people can handle it, I would go with Merge Sort. Because merge sort is efficient, stable, and teaches several important concepts (merging, divide and conquer).
Selection Sort:
Find the minimum/maximum value and put it in place, then do it again on the rest of the list...this is very intuitive. For me selection is much more intuitive than even bubble sort. You could probably teach this in very little time. And there will be a feeling of accomplishment by people implementing this... Although Bubble and Insertion can quit early and will not waste time on a sorted list. Selection is probably the easiest to do. Insertion is probably the hardest to implement.
MergeSort:
This will teach how to merge (which is important because there are a ton of speedups you can get by merging two sorted lists together) as well as how to divide the problem into smaller sub problems (important for dealing with hierarchical structures and also used in quick sort). QuickSort though faster is much harder to understand. You need two scanning variables, a pivot item, etc... Merge is more straight forward and merging will come in handy for things other than sorting (like joining two records together that are sorted on a field)....
The basic concept of a merge is intuitive. Take the lesser item from a sorted list and put that in the final list. And dividing the merge sort problem up is also kind of intuitive.
mergesort(first half)
mergesort(second half)
merge (first half, second half)
If you can only teach one sort and have to do it quickly (or the audience isn't really interested at all) I would tend towards Selection because this is harder and selection could be taught quickly. But if the audience is more motivated then I would do Merge because it teaches so many additional fundamental concepts.
Of the more efficient sorts this one is much easier than quick and heap sort. Although quick sort is probably the quickest in practice (as long as you have plenty of ram) and heap is probably able to sort the largest lists (if implemented non recursively).
Bucket Sort:
I would touch on this because it is also intuitive and represents another type of sorting algorithm. In many situations this is appropriate and the O(n) time is very attractive.
Counting Sort:
It has its uses. There are some cases where this is very efficient...It is also relatively easy.
