Lady Gryphon, you don't need to worry about system requirements with most of those games, since they're old. Even newer adventure games don't require that much hardware to run, like Machinarium.
I also really loved The Longest Journey. I loved the story and the character of April Ryan, and the worlds of Stark and Arcadia. Did you know it has a sequel, Dreamfall?
Monkey Island games are probably best played in order. The new episodes make up the 5th part of the series. The first game The Secret of Monkey Island, which is possibly the best one, was fairly recently remade and it's for sale on Steam as well as for the Xbox Live Arcade. It's nine dollars in Steam: http://store.steampowered.com/app/32360/
The Secret of Monkey Island is one of those rare games that constantly kept me laughing out loud. There's so many great moments in there. And I really want a T-shirt that says "I found the Secret Treasure of Meleé Island (TM) and all I got was this stupid T-shirt."
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