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.
I love it when two things that I adore find each other out in nature and create some kind of apotheosis such as this. Truly, the fruit and flower of life.