So many great movies, so little time. 🙂 Some of my favorites have already been mentioned: Das Boot, Touch of Evil, Chinatown, The Man Who Would be King, Greenaway's Cook/Thief/Wife/Lover (although I prefer Belly of an Architect).
Rather than follow OP instructions, I'll mention three movies with strong storyline and aesthetics both. Third place is "The Elephant Man" by Lynch. Shot in B&W, John Hurt must emote behind heavy makeup: awesome cast, all around. Second place is "The Emerald Forest" by John Boorman which was way ahead of its time for covering environmental/cultural destruction: a visual feast with pace.
First place is "Der Untergang" which I saw four times on the big screen, and it left me badly shaken every time. This is not entertainment, but a window into history, a place so horrifying that it's hard to believe it happened. For those unfamiliar, this movie tracks the last ten days of Hitler (channeled by the awesome Bruno Ganz) and his Bunker denizens. The aesthetics are oriented to academic authenticity and perfectly transparent presentation. The Continental cast is very strong, with special mention for actress Corinna Harfouch: her Magda Goebbels is heartwrenching to watch, and made her sick to portray.