Iron Maiden

Bad Religion

Slayer

Misfits

Black Sabbath

Faith No More

Fugazi

I could go on but from you list, those come to mind

Depends on how you define classics, but Sabbath is a must listen, in every incarnation they've had.

I'd suggest Deep Purple as well, maybe some Steppenwolf and Iron Butterfly

You've got bands like Maiden that you have to listen to at least once. Judas Priest is in that category as well, imo.

If you like thrash, then try some exodus, anthrax, megadeth, overkill, kreator and testament

Sepultura is kinda like pantera in that they blend genres a lot, and both are kinda central the the post-80s metal wave.

Fucking motorhead. That's all that needs to be said

Saxon is a cornerstone band. Nwobhm wouldn't have been the same without them

If you want darker/heavier stuff, Death is often cited as the forefront of death metal (though I don't agree). Cannibal Corpse goes back a ways far enough to be a classic band. Dimmu Borgir for the blacker side of things, and I think if you like Bathory, you'll love Dimmu Borgir.

Fuck, I can't not recommend Amon Amarth. Fucking gods of metal.

I'm trying to stick to stuff that's been around long enough to be considered classic, and is also fairly accessible in terms of how far down the rabbit hole you'd be climbing. There's a lot of bands that are essentially formative to one subgenre or another, but don't really hit for most people, or are hard to find to listen to.

Hell, you've got stuff like burzum that essentially founded a subgenre, but kinda suck enough that even some fans of that subgenre don't really listen to more than once.

But, yeah, it really depends on what kind of "classic" you're looking for, and whether you want the stuff that tends to be widely loved, or a more niche experience.

Anthrax

Dio

Slayer

Rainbow

Megadeth

Misfits

Nightwish

Candlemass

Crypta (They'll be considered classics when enough time has passed IMO).

Pantera

Exodus

Megadeth

Fear Factory

Napalm Death

Iron Maiden, Saxon, Motorhead, and Black Sabbath.

First things first; not everyone is suggesting Death, which means that not enough people are suggesting Death.

If I'm going off of your list with the angle that I am wanting to suggest more stuff that you might like that are classics I'd go with stuff like mid-80's through mid-90's period Pestilence, Gorguts, Exhorder, Coroner, Kreator, Nihilist, etc. Someone mentioned Napalm Death earlier, and that's probably not a bad rec for you.

If I'm just wanting to throw out some stuff that I consider to be classic without regard to your list I'm going with stuff like Suffocation - Pierced From Within, Dissection - Storm of the Light's Bane, Cryptopsy - None So Vile, My Dying Bride - Turn Loose the Swans, Ulver - Bergtatt, Hypocrisy - Hypocrisy, Mayhem - De Mysteriis Dom Sathanas, Edge of Sanity - Crimson, Meshuggah - Destroy Erase Improve, Samael - Ceremony of Opposites, ...there's a lot, and it's not hard to keep going.

Something that's cool about metal is it's history of being an underground art form. Tape trading scenes, indie zines, and basement headshops being the places to find out about different stuff. A lot of people have different ideas about what constitutes classics based on where they're from, and at what point they entered into the fray. Even with the internet granting access to virtually everything, there still really isn't consensus on a question like this, and the fandom remains seemingly immune to homogeneity. That's fucking awesome. Discovering what you like is a big part of the fun. Enjoy.

Rainbow (and Dio), Danzig, and Korn. Disturbed and Godsmack also go hard as fuck.

Sepultura and Sarcófago

Less known band, but I head banged hard to Accept in my teen years for a short spell. Balls to the Wall was their big single but I remember liking most their stuff short a short time.

If you like Possessed / death metal, give early Swedish death metal a try! Entombed’s debut album “Left Hand Path” (1990) and Dismember’s debut “Like An Ever Flowing Stream (1991).

Anvil deserves to be on this list.

Just to add some I don’t see already mentioned:

Opeth, Anthrax, Kreator, Rammstein, System of a Down, Static X, In Flames

I'll add a few.

Death

Pentagram

Atomic Rooster

Cirith Ungol.

Some unmentioned: Darkthrone, Emperor, Blood Incantation, Sleep Edit:Blood Incantation is relatively new

Killswitch Engage

Avenged Sevenfold

SOAD

Five Finger Death Punch

Bullet For My Valentine

Children of Bodom

Slipknot

Lamb of God

white zombie?

Bad Brains

Meshuggah, early Mastodon, Death, Slayer.