I would say the very first game to get is Gran Turismo 3 A-Spec. At the $19.99 Greatest Hits price, you really can't go wrong. When I got my PS2 a couple years ago, GT3 came with the system as a "special edition" package. It's probably one of the best games to be packed in with the system, because the game had so much depth, gameplay and many lost hours poured into it.
Some other games I would suggest are: Amplitude, Silent Hill 2 and 3 (you might want to pick up the first one if you haven't played it, and tackle that before 2 and 3 to really understand the story and referrences), Ace Combat 04, Virtua Fighter Evolution, Tokyo Extreme Racer 3 (I really like it, I'm not sure how other people like it's design), and SSX 3 (I have the GC version, and it's fantastic). I haven't been playing my PS2 as much as my GC (despite having it longer), so I'm still looking around for games that would interest me as well.
And be sure to get a memory card!