Game look very interesting and addicting however I have a few questions for the veterans and Diablo fans.

1. I haven't played Diablo I & II, will I get the hang of the game play and storyline easily?

2. Do you recommend I play the single player first then start playing online?

3. My computer isn't amazing. It has a 512mb Nvidia graphics card, 4GB ram, 2.7gz processor and Intel dual core (or something like that), will the game still run smoothly?

Thanks in advance guys!

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1. I haven't played the first and I've played probably just the first act of Diablo II, but a long time ago and I hung on the game play, so yes.

2. If you never played Diablo, go play in single player, then switch to online when you'll know how it works and such... It's always better :P

3. Check your graphics card, as you didn't specify which one it was :/

With what you already gave, you fit in their recommended requirements, though here's a the minimal requirements chart, so you can check if your graphics' card is good enough:

1. I haven't played Diablo I & II, will I get the hang of the game play and storyline easily?
The story might confuse you a bit, but I would suggest watching this video (here) to catch up quickly. As for the gameplay you should have no problem getting into it. Its fast paced, and caters to both casual and hardcore gamers.

2. Do you recommend I play the single player first then start playing online?
Yes. Online can be very "choppy". What I mean by that is you may be skimping out on little tidbits of the game because people in your party have already done it. Plus you're going to want to get a hang of the story/gameplay first before you jump right in with other people.

3. My computer isn't amazing. It has a 512mb Nvidia graphics card, 4GB ram, 2.7gz processor and Intel dual core (or something like that), will the game still run smoothly?
Oh yes, your computer will run it perfectly. Maybe not on the highest graphics, but you should have no problem.