I will try to use your categories, but I'm not a classical or jazz fan so leaving out them altogether and adding my own Modern Music (post 2010) category. It was
very difficult to list only 30.

Blues:
Skip James: Hard Time Killing Floor Blues
Mississippi Fred McDowell: I Do Not Play No Rock and Roll
Mississippi John Hurt: The Immortal
Howlin' Wolf: Moanin' In The Moonlight
Country (also not a big country guy except one artist

):
Johnny Cash: American III Solitary Man
Johnny Cash: American IV The Man Comes Around
Hip Hop:
Public Enemy: Fear of a Black Planet
Beastie Boys: Ill Communication
Modern Music (post 2010):
The Asteroids Galaxy Tour: Out of Frequency
CSS: La Liberacion
The Pack A.D.: Funeral Mixtape
Ladyhawke: Anxiety
Rock:
U2: The Unforgettable Fire
Rolling Stones: Let it Bleed
Dorothy: ROCKISDEAD
The Doors: Waiting for the Sun
Prince: The Dawn (bootleg, but counts!)
Rock (alternative):
The Dead Weather: Horehound
Arctic Monkeys: Whatever People Say I Am, That's What I'm Not
Cure: Kiss Me, Kiss Me, Kiss Me
The Smiths: The Queen is Dead
Peter Murphy: Deep
Yeah Yeah Yeahs: It's Blitz!
Sinead O'Connor: The Lion and the Cobra
The Libertines: Libertines
PJ Harvey: Stories From The City, Stories From The Sea
Rock (metal):
Rammstein: Herzeleid
Ministry: The Mind Is A Terrible Thing To Taste
Singer/Songwriter:
Suzanne Vega: 99.9 F
Peter Doherty: Grace/Wastelands