Hmm, interesting question. I think it would be more important to get a variety of sounds than just their best songs. Here's what would be a good mixture.
-I Will Follow (Edge's ringing guitar)
-Tomorrow (most Irish sounding tune, bagpipes add variety)
-October (piano-only song)
-New Year's Day (great transition between piano and guitar)
-Sunday Bloody Sunday (the drums and to show off a political rock song)
-Wire (crazy guitar)
-The Unforgettable Fire (for the amount of backing instruments)
-Where the Streets Have No Name (synth-based intro, simply because it shows musical perfection)
-ISHFWILF from Rattle and Hum (gospel)
-WOWY (shows off the bass guitar, other-worldly quality)
-One Tree Hill (another but different other-worldly song)
-Desire (American southern rock)
-God Part 2 (for the drums)
-When Love Comes To Town (for the blues and B.B. King)
-Zoo Station (makes your speakers sound like they're exploding in the beginning, Bono's distorted voice)
-The Fly (industrial rock, Edge's guitar solo)
-Mysterious Ways (funky guitar work)
-Love is Blindness (for the organ)
-Zooropa (three songs combined into one)
-Numb (Edge's rap)
-Lemon (Bono's falsetto, very groovy guitar)
-The Wanderer (Johnny Cash)
-One live from Modena (rock song with an orchestra)
-Mofo (just for that guitar work)
-The Playboy Mansion (for the slide guitar work)
-Beautiful Day (for that U2 rock quality)
-Elevation (Edge's guitar, Bono's whooping)
-Acoustic Stuck (stripped-down rock)
-Vertigo (pure, hard rock)
..the song
