I'd probably pick Moonlight Sonata.
GG`s maternal grandfather was a cousin of Grieg so maybe that`s why.For me the Grieg Sonata. My favorite recording of the Grieg is by Glenn Gould which is interesting as Gould wasn't known for being a champion of those very pretty and decorative High Romantic composers and Gould recorded very little Chopin, Mendelssohn, or Schumann; and yet Gould's Grieg recording is very fine.
I'm not keen either. Having sampled some of the recommendations so far (those that I didn't already know by LvB) I'm inclined to recommend Berg's no. 1.A genre that I am not crazy about (in general, I care less for solo piano than most TC members). I'd probably go for Beethoven's Piano Sonata No. 8 in C minor "Pathétique".