Great games for the PS3:
Uncharted 1 and 2. I would highly recommend playing Uncharted 1 first, as it's really cheap and then move to 2. If you play the first one, you'll have a much, much greater appreciation for how well done the second one is. It's just an amazing game.
God of War Collection is a must if you haven't played the first 2. Then move to GoW III.
If you missed out, Fallout 3 is great. Just great.
If you're an RPG fan, I would recommend Valkyria Chronicles. It's a great game.
Ratchet and Clank games are always amazing if you want a platformer.
Oh, and the following game I cannot recommend enough:
LittleBigPlanet. It's amazing. Simply astounding. If you can get online with your PS3, you have access to over 3 million user created levels. Some of them are just breathtaking. I would definitely get this title. It's roughly 30 bucks for a used copy at GameStop and I would invest in it. You can beat the story mode in a few hours, but the millions of levels you can play online are awesome. Someone actually recreated the entire NES game of Contra as well as the entire first NES Super Mario Bros. game. The things people can come up with are unreal.
Those are some titles to get you started.