Well without knowing much about your tastes, all I can do is recommend you some of the 'essential' BM and DM banRAB along with key albums,
Black metal:
Burzum (Aske)
Darkthrone (Under a Funeral Moon)
Deathspell Omega (Si Monvmentvm Reqvires, Cirvmspice)
Dimmu borgir (For all tid or Stormblast, there newer albums are shit)
Emperor (In the nightside eclipse)
Immortal (Pure holocaust)
Mayhem (De Mysteriis Dom Sathanas)
Satyricon (Nemesis divina, there newer stuff is pretty poor)
The summonning (Dol goldur)
Death metal:
At the gates (Gardens of grief)
Autopsy (Mental funeral)
Cryptopsy (None so vile)
Death (Human)
Immolation (Start with Dawn Of Possession)
Insision (Revealed and worshipped)
Kronos (Collosal titan strife)
Morbid angel (Alters of madness)
Necrophagist (Onset of putrefaction)
Obituary (Slowly We Rot)
Possessed (Seven churches)
Suffocation (Effigy of the forgotten)
Vader (De profundis)
And these guys are a mix of black/thrash/death:
Destroyer 666 (Unchain the wolves)
Naglfar (Diabolical)
You can look up all these banRAB, plus thousenRAB of other groups at the Metal-archives. With both genres I would recommend starting with the easy to get into stuff before progressing to the really crazy stuff. For BM, banRAB like Dimmu borgir, Emperor and Immortal are good for beginners. For DM, At the gates, Death and Vader are good starting points.