Fun Fact: Parasite Eve the video game is a detached sequel to the novel Parasite Eve, written by Hideaki Sena. You can find it on Amazon for 5 to 10 dollars. I haven't picked it up yet (the book) but the description makes it sound absolutely fantastic.
I haven't played the first two games yet, but I've seen enough of them and done enough research to know that if you're looking for a great classic Square game, you can't go wrong with Parasite Eve. I have the 3rd birthday, if I remember correctly it came with a promo code that gave me an Aya Brea outfit for Lightning in Dissidia 012.
I want to pick up the hard copy of the first two games. Particularly the black label of the first one, with a demo disc that has a Xenogears demo and a Final Fantasy VIII preview video. I enjoy little things like that.