I have the Diablo for Playstation. It's pretty garbage. The only good thing about it is there's TONS of lore and extras and shit on the disc.

Play the Diablo for PC. There's an "expansion" of sorts, Hellfire, which wasn't made by Blizzard, but by Sierra. I don't really care much for Hellfire, but it's enjoyable in its own way. Play them like two separate games.

Diablo 2 is a great game online or off. I suggest you play online regardless of whether or not you play with other people, since you can get Ladder only items if you play on Ladder. Definitely get the expansion, Lord of Destruction, and play it primarily. It might be good for you to start with just Diablo 2, since that's what everyone started with. You'll appreciate the differences of the expansion more that way, I guess.