I learned Bubble Sort first -- I think if you do only one, you probably need to do one of the O(n^2) algorithms because they are easier to understand.
There are a lot of sort visualizers out there to help quickly show a comparison:
- http://www.cs.ubc.ca/~harrison/Java/sorting-demo.html
- http://math.hws.edu/TMCM/java/xSortLab/
- http://vision.bc.edu/~dmartin/teaching/sorting/anim-html/all.html
- http://maven.smith.edu/~thiebaut/java/sort/