My first metal album was S.E.T.I. by The Kovenant, who by then were in the realms of industrial, but whom I traced back to their black metal roots and discovered Arcturus and Dimmu Borgir. From those two I discovered Borknagar, which remains to this day my all-time favorite black metal band. Quintessence was the first black metal album I ever bought (along with The Archaic Course and Arcturus' Sideshow Symphonies -- all albums with Vortex on lead vocals).
My first introduction to death metal was through cookiecutter when he had me listen to "Roswell 47", leading me to download a few other Hypocrisy songs. CC sent me on an errand one day to pick up Hypocrisy's Virus for him, which I took the songs from to be the first death metal album I heard in full.
I'm not quite sure which was my first own death metal album, but likely it's either Dark Tranquillity's Character (another band I thank CC for showing me), Zyklon's Aeon, or In Flames' The Jester Race. Since then I've sold all my In Flames albums except for that one, Dark Tranquillity remains the only Gothenburg band worthy of my ears, and Zyklon is still one of my favorite death metal bands (though World ov Worms, my favorite album by them, I classify more as black metal).