mayhem, mortician, cannibal corpse, devildriver, anal cunt, anal blast, belphegor, behemoth, carcass, burning inside, deathwitch, hemmorhage, impaled, regurgitation, and there are countless more. I own over 2000 cds now, so if you need more help, let me know

As far as those specific genres I don't know how much I can help as far as suggestions, but as far as metal in general I recently discovered 3 Inches of Blood (even though the've been around for quite a while) and fell in LOVE with them, they kick so much ass, If you like The Sword you might also like Wolfmother and Empress. I dunno if you'd call them straight up metal, but they've got some classic rock/punk influence, but Valient Thorr is the SHIT. Uhm.. I'll just start naming awesome Metal bands that everyone needs to hear, you'll probably already have a lot of these but...Black Sabbath (give them a second look, some people don't give them the credit they deserve, and you can always find some of their stuff you might not have heard before) Mastodon, Avenged Sevenfold, Five Finger Death Punch, Lamb of God, Sleep (great stoner metal, they do a killer cover of Sabbath's Lord of this world), Clutch, High On Fire, Orange Goblin, Melvins (they get kinda sludgy sometimes), S.O.D. (Stormtroopers Of Death), Solace, In Flames, Entombed, Venom, Pig Destroyer, Otep, The Mentors are good for a laugh, lol that's about it unless I should mention the obvious ones hope that helps.

For Black Metal...
for what are considered the main bands to come out of the second wave in the early 90's:
Mayhem, Darkthrone, Burzum, Emperor, Gorgoroth, Dark Funeral, Satyricon, Handful of Hate.
Check out Watain, Ludicra, and Wolves In The Throne Room as well.
Fucking avoid the shit like Cradle of Filth and if you want a laugh there's Crimson Moonlight and Horde that are self-professed christian black metal

Death Metal (sneaking some grindcore in):
Behemoth- Later albums like Demigod serve as quite the perfect amalgamation of black and death metal.
Blood Red Throne- another worthy mix of the two genres. Has Tchort of Emperor fame
Cannibal Corpse, Morbid Angel, Deicide- Flordia stalwarts that started in the 80's and are still going
Impaled- SF deathgrind that perfectly mixes intellect, pyrotechnics, and sarcasm.
Phobia- CA Anarchist grindcore that's shared a few members with Impaled
Rotten Sound- Finnish Political grind
Bloodbath- Swedish melodic death surprisingly delivered by members of Opeth and Katatonia.
Coldworker- Swedish death metal formed by Anders Jakobson previously of Nasum
Braindrill- Brutal death metal from Santa Cruz, California
Hour of Penance- Italian death metal
Suffocation- Technical death kings hailing from New York
Deeds of Flesh, Decrepit Birth, Vile, Severed Savior- All California death metal bands on Unique Leader Records
Entombed- Swedish death metal that influnced bands like Bloodbath but has been around long enough that
their cover album included tracks by bands like Husker Du, Bad Brains, Jerry's Kids, and Repulsion
Misery Index- a political death metal mutt influnced by everything from Morbid Angel to His Hero Is Gone.
Featuring ex-members from Dying Fetus.
Napalm Death- although now death metal is now injected into the music, drummer Mick Harris was the one to
coin the term 'grindcore' and the started off touring the UK with bands like the Subhumans
Benediction- British death metal that featured Barney from Napalm Death on their earliest work
Assuck- anarchist grindcore
Leng Tch'e- Used to feature the vocalist from Aborted on drums. Check out Marasmus
Nile- Egyptian themed death metal
Ratos De Porao- Brazilian death thrash that did a few tracks with Sepultura

And just because it's a weird combination though you didn't ask for it, Ensiferum and Equilibrium are two folk metal bands worth checking out. Let me know what metal bands you're into besides the three listed and I could be a bit more precise with my recommendations