Well here are my thoughts.
If this is a competition I may have different ideas, but if this is just a recital I would recommend as follows.
1) The Polonaise could be nice, but it is pretty over played and doesn't seem to follow well with the Bach either Key or mood wise.
2) This I think would be a really good idea. It is the most uplifting of the pieces that you have listed although, depending on your audience, it could be a bit unknown.
3) Sorry to say, but I do not like the Hungarian Rhapsodies. If I had to pick one I would say 6 or 12. Either would work fine, but personally I would do the Brahms.
4) The Rachmaninov is a piece I adore. I have played it many times and plan to play it many more times. In my opinion it works best as a whole (i.e. all three mvts.) The first mvt, is a little longer than you need anyway. Also it has a soft almost incomplete ending (that transitions perfectly into the 2nd mvt! I love this piece), so while I think it is a great piece I am not sure it is what you are looking for. It is crazy hard too!
Have you thought at all about a Chopin Ballade (maybe the 3rd) or the Scherzi (I would suggest the 4th)? If not those maybe the Liszt Mephisto or the 2nd Ballade.
Hope that helps a little.