What nationality are you - living composers in your country would love some exposure.
How on earth do you finish an undergraduate degree in music and not have a list of stuff a mile long that you are just dying to get into??
This one's my suggestion as well.Also, I would recommend to set a goal of learning any complete opus you like of a composer, lets say Chopin's 24 preludes, his 24 etudes, or Prokofiev's complete Visions Fugitive, etc, start building your repertoire with stuff you like, piano concertos as well.
This is exactly the problem. I have a list of pieces, but I'm afraid of overreaching where I am currently with my technique.