Just to share a few words of advice from my boss, who is a recent Woodrow Wilson School MPA graduate and sat on their admissions committee:
Getting into WWS is NEVER guaranteed, no matter how good you are. It is a very small program and it uses an extremely hands-on method to "build a class", so there is always a decent chance that if your profile is too similar to someone else's profile, then one of you is booted, even if you're both objectively amazing.
WWS is free. They don't like to advertise that because they want people who truly want to be there regardless of price, but it is indeed free. Your food, housing, and stipend are provided by the school. Even your summer is funded so that you can walk into pretty much any organization you want and offer yourself as free help. So, what does that mean for admissions? It's REALLY hard to get in and tons of brilliant people get rejection letters, so don't feel bad!