Matt, I'd check out Yojimbo, without which there would have been no Fistful of Dollars or Clint Eastwood as a major movie star.
Rashomon is important as a movie which deals with the many perceptions of "truth".
The Hidden Fortress since the plot and characters are funny, and because of its influence on Star Wars.
Although not directed by Kurosawa, Mifune's depiction of Miyamoto Musashi in the Samurai Trilogy is so compelling that I watched all three one after another.
The Challenge is only worth watching since Mifune's head gets split down the middle in the film, but the halves rebound back due to their rubber nature. I hope he got paid a lot for his role in that movie.