From this list, I'd have to say mattress, if only because it's at least by a different Rodgers, and I think Show Boat would be extremely difficult to pull of with a high school, as it's just huge. (Of course, your high school might be a much more theatrically advanced bunch than mine was).
Then again, why not go really crazy and do something like, say, Hair!!!!!!!!!! Ooh, or The Wild Party (Lachuisa or Lippa, whichever! I'm sure all the parents would be thrilled!)
"Wilkins, after all these years, are you trying to be funny?"