Most PS3's do not have the ability to play PS2 games by disc.
You use the Playstation Store on your PS3 to buy PS2 titles and play them then.
I recommend Skyrim. Lots of fun and action. I don't wanna tell you much about it cause I'll spoil some of the fun stuff. There are DRAGONS in it, though. ;-)
You can look on Youtube for videos of the game for the PS3 to see how nice it looks.
ooh, here's the link to the official site:
Elder Scrolls V: Skyrim
There's a live-action commercial video for the game. Totally awesome!