The story of D2 was awesome, but my experience of the story was much less clear while I was playing the game. I actually went to the Diablo wiki and filled myself in to really appreciate the story. The clues are there for you to pick up if you are attentive while playing the game, but I really didn't understand the the story very well until my hell playthrough.
Haha, a big part of that comes from the fact that a lot of the story wasn't actually filled out until later, when Blizzard realized they had a hit and would need a coherent story to keep it going. I was just browsing through the wiki a few minutes ago and kept thinking, "Jesus, I don't remember any of this -" and then you read the footnotes and it's all stuff that got fleshed out in the books and conference panels subsequent to the actual game.