@AC Slaughter first let me explain my philosophy, which is simple. The only way to understand context, growth, change, is to start at the beginning. Full stop. It'd be like being told to listen to [insert modern stoner/doom band] before Black Sabbath. IMHO, it's far easier to discover what you like/don't like than by haphazardly looking at albums from all over. Sometimes it works to do so, but more often than not you hear latter day In Flames and then skip the early stuff. Whoopsie.
Now with death metal it's a little different; a lot of the really progressive and/or more technical stuff was happening at the same time that the more traditional, old-school stuff was also taking root. Really interesting to be honest. Old school death metal (OSDM) was born from thrash, so it's basically here's a riff. Get in the pit or get out of the way. Whereas the more technical/progressive side of things is surely more complex and nuanced, but at the expense of fucking headbanging (usually).
Ok, that said, I'd go in this order (of the 2 lists):
Death - Leprosy
Entombed - Left Hand Path
Dismember - Like An Everflowing Stream
Pestilence- Spheres
Morbid Angel - Altars of Madness
Cynic - Focus
Grave - Into the Grave
Entombed - Clandestine
Massacre - From Beyond
Obituary - Cause of Death
Deicide - s/t
Bolt Thrower - War Master (or Reign in Chaos also works)
At the Gates - Slaughter of the Soul
Carcass - Heartwork
In Flames - The Jester Race
Suffocation - Pierced From Within
Gorguts - Obscura
Nile - Amongst the Catacombs...
Opeth -Still Life