Hi OP.
As a fellow metal head of the same age with a similar background in my teens of thrash metal, allow me to add my two penneth of classic death metal albums. I've selected these as being the albums that you will probably be able to relate to most easily from your background while allowing entry into the wider realms of death metal.
1. Bolt Thrower - ...For Victory. Emminently hummable, mid-tempo war-obsessed English death metal with some doomish elements here and there.
2. Carcass - Heartwork. "Necroticism" is by far the better album, but not nearly as easy to listen to if you are new to death metal. Neatly kicked off the whole melodic death metal kick.
3. Obituary - Slowly We Rot. Once you've heard John Tardy sing, you'll shit bricks, to quote the cool kids.
4. Death - Scream Bloody Gore. Basically noisy thrash with deathly atmosphere.
5. Entombed - Wolverine Blues. By now, Entombed had moved into "Death n Roll", but as entry level listenable extreme metal, it does the trick admirably.
6. At The Gates - Terminal Spirit Disease. Melodic - also less annoying than Slaughter Of The Soul.
7. Morbid Angel - Domination. Not their best, but certainly their most accessible.
8. Napalm Death - Enslavement Through Obliteration. When grind succumbed to death metal.
9. Vader - De Profundis. Like Slayer ? Think their output since Seasons in the Abyss has been dogshit ? Me too. Try this - basically Slayer inspired death metal.
10. Deicide - Serpents of the Light. Incredibly catchy songwriting combined with cartoonish hatred of Christianity. What's not to like ?