I just had my HP PC rebuilt and I'm interested in getting TES anthology. I have Skyrim for Xbox with countless hours, including Dawngaurd DLC, and I've played a little bit of Morrowind as a kid on the computer.
But I want the full series.

But the question is, is Arena and Daggerfall still playable after Skyrim?
And another question, is a normal HP laptop able to run Morrowind, Oblivion, and more hopefully, Skyrim?

Both Daggerfall and Arena are still playable, but they are very diffrent games with diffrent philosophy behind them. If you are asking if they are like new Elder scrolls then the answer is no .

Let's use http://www.gamesas.com/topic/1481886-thinking-of-getting-all-es-main-titles/ you posted on the same topic.