The easy choices have no comments, but I've added a couple notes on the ones I puzzled over for a minute or two.
This was far, far easier than simply picking favorites. Were the constraints much more limiting, making my choices automatic?
American Analog Set - The Golden Band 
Bach, Johann Sebastian - The Art of Fugue, BWV080; Musical Offering, BWV079 (2)
Coltrane, John - Giant Steps 
Davis, Miles - Bitches Brew (Remaster) (2)
Eno, Brian - Ambient / Music for Airports 
Fugazi - Red Medicine 
Godspeed You Black Emperor! - F#A# 
Hum - Downward is Heavenward 
I
Jawbox - My Scrapbook of Fatal Accidents 
King Crimson - Larks' Tongues in Aspic 
Low - The Curtain Hits the Cast 
Massive Attack - Protection 
Nirvana - Nevermind [Leaning toward Neutral Milk Hotel but in the end I went with the old favorite.]
Olivia Tremor Control - Black Foliage Volume I 
Pixies - Surfer Rosa [Terrible letter. Lots of I'm-not-sure-choices.]
Q
Rush - Moving Pictures 
Spiritualized - Lazer Guided Melodies 
Tribe Called Quest, A - The Low End Theory [Tough because I like a few roughly as well as one another - Tricky, Tortoise, Tangerine Dream. But Tribe wins out because they feel slightly more fun today.]
University of Northern Iowa Jazz Band One - That Big Band Thing [A sparse letter. And a good album, but I'd be disappointed if I were U2.] 
Vangelis - Blade Runner [The Velvets are for me, at the moment, a singles band.]
Waits, Tom - Rain Dogs 
X
Yo La Tengo - I Can Hear the Heart Beating as One 
Zappa, Frank - Apostrophe'/Overnite Sensation [Mr. Zorn is creeping up on Papa Zappa, though.]
mu-Ziq - Lunatic Harness [Yes! A free letter!]