Well, it's not PS2 only but the Grand Theft Auto games are certainly worth it IMO. GTA3 and Vice City are available at bargain prices and provides heaps of fun. I just love playing this game with friends, alternating between players after each succesfull/unsuccesfull mission, 5 secret packages gathered etc. It's just fun to see your friends crash/get shot/explode/whatever after which somebody else can try and prove he's better and get laughed at. GTA San Andreas is actually the worst of the 3 IMO, I find the area is just too big and the map lay-out of the cities is rather uninspiring.
Another game I can recommend for the PS2 is Kingdom Hearts. At first the game looks targeted at kids, I mean, Final Fantasy and Disney mix? A manga boy character goes and adventures with Donald and Goofy so they can together find the boy's lost friends and the missing King Mickey while defeating the evil that threatens everything?
Actually it's a great game and it's quite hard as well. Most kids will probably fail at making it halfway through the game. The worlds you go to are all nice Disney settings with some good level lay-outs. Familiar characters from the Final Fantasy games are included and they help to stop the game from becoming an all Disney fest. The game storyboard is clearly also by Square which keeps it from being lame.
The one thing that's not so great is the Gummiship thing. Build or improve your own space ship with building parts gathered and blast your way through the shooting parts connecting levels. Sounds nice eh? It could be, if only the very first space ship you're given wasn't able to shoot its way through all enemies even at the flight towards the last level. It's not the fault of the ship and it's puny laser but the easyness with which you can defeat your enemies during those shooting bits and their inability to hit you (most damage stems from you flying into obstacles, not from getting shot at). But this is only a minor detail as you only need to do this once to get to a new level and afterwards you can simply warp to it in one go.
So that's 3 games with excellent playing value which shouldn't cost you more than $60 total. Check 'm out!
Edit: Darn, only just noticed the 'FPS' part in your subject title!
Oh well, if you want other great games on the PS2 that aren't FPS' try the ones I recommended!