John, I've found that I have the best luck when I choose images that look like they have something in common...like they belong to the same body of work. In other words, instead of choosing three that show the range of my work, I would choose three that all have the same "feel."
I agree that this is really hard, because as someone said above, you never know what is going to appeal to any particular judge. Doing this with my own images drives me crazy, so I understand how you feel!
Best of luck!