Oh, you're getting a PS3? I can help. <---- PS3 fan boy.
Okay, now for your games here's what you should get.
Ratchet and Clank Future series
If you were a fan of R&C back on the PS2 then you need to pick of the successor series Ratchet and Clank Future. If you're unfamiliar with the PS2 series, it's okay. The Future series is a completely new story line. Now, the R&C games (once again, if you're unfamiliar with the series) follows the adventures of Ratchet and his little robot friend Clank. The PS2 series was a simple, episodic cartoony shoot-'em-up platformer from the makers of the original Spyro tirlogy back on the Playstation 1. This time around, the series has a continuing storyline. The first game, Ratchet and Clank Future: Tools of Destruction primarily focuses around Ratchet and he learns the truth behind the Lombax race, which is the last of. The second game, The Quest For Booty (title makes more sense when you play the game) is a bridge game that fills the gap between Tools of Destruction and it's sequel, Ratchet and Clank Future: A Crack in Time. Crack in Time picks up where Tools of Destruction Left off and, well, I'm not going to spoil anything. The Ratchet and Clank Future series is like playing a Pixstar movie in both presentation, tone and style. The game may have a good amount of story in it that you can take seriously, but it manages to be funny and enjoyable all at the same time.
Resistance series
Made by the same company that did Ratchet and Clank, Resistance is pretty much the Halo of the PS3. Putting my fanboyism aside, the Resistance games are pretty solid FPS games that make up for unoriginality by just being tons of fun to play (Resistance 2's co-op is magical). As far as concept goes, it's about an alternate history 1950s in which an alien race called the Chimera by the humans is coming down to destroy our tiny human brains and it is up to Nathan Hale, who is resistant to the Chimeran virus (forgot to mention, they can infect you and turn you into a Chimera) to save the world! While standard, the fun and enjoyable single player and multiplayer makes up for it. This is a must-own for just about any Playstation 3 owner.
Uncharted series
A Tomb Raider for a modern age. Uncharted follows the life of treasure hunter Nathan Drake as he travels around the world in search for treasure. The first game was all about the single-player experience, no multiplayer at all. But don't be turned away by this, Uncharted: Drake's Fortune delivered on platforming, combat, puzzles, everything. And you know what? It may rip-off Gears of War in terms of combat, but it did it better. Drake doesn't control like cow operating a forklift, you don't have different button assigned to roll into different cover and such. For Uncharted, it's just the circle button and the control stick. Oh yes, and the story, while standard, was enjoyable. Now while the first Uncharted was good, it's sequel blew it out of the water (except for the puzzles, it failed epically on those). This time around the single player game was slightly longer, and entirely new adventure and we got some multiplayer. And unlike most FPS', the single player didn't get screwed over because of the multiplayer. I can gladly tell you that for the most part, Uncharted 2's campaign was an excellent experience and the game added in excellent mutliplayer to complement it. If you have a PS3, and you don't have the Uncharteds, then boy are you missing out.
Infamous
Imagine that one day you received incredible power, and that you live in a decaying dystopia that was falling into madness. What would you do with that power? Would you became a savior to the citizens of this city or would you simply make it into your playground as you, a god amongst men, simple destroy these inferior humans? Welcome to Infamous, in which you take the role of a man who encounters questions like these when he gains power over electricity. The story is surprisingly good, the game play is incredibly fun, the world is varied and interesting and there is a ton to do in it. If you heard good thing about Infamous, it's because all of it is true. With a ton of side-missions, a hero and villain story along with a ton of collectibles Infamous is a game that's worth playing more than once. And it's also just a lot of fun to play, wither you scaling a tower, saving a civilian or frying that same civilian alive, there's allways fun to be had with Infamous.
Other games
And that's just the tip of the iceberg! If you can stand the story, then Metal Gear Solid 4 is worth taking a look at (although I'm not a big fan of the Metal Gear series), Little Big Planet is pretty much classic platforming remade for a modern generation of gaming, and (even though I really don't like it), you may find Killzone 2 to be an enjoyable ride.
Now, this is already really long so I'm not going to get into this too much, but some mutli-console games that are worth looking into if you didn't get them on the 360 includes BlazBlue for fans of 2D fighting, Prince of Persia if you want to be assaulted by incredible graphics and great game play, and plenty more than that.
Online
Playstation uses something called the Playstation Network for their online service. And it's free. Yes, unlike Microsoft, you get to play your games online for free. Although if you like to interact with the guy you just teabaged don't expect much of a response. While Xbox Live is full to the brim, Playstation Network is silent as the grave. How this will affect your experance will change for person to person, but for me, I personally perfer it.
The Playstation Store
This is where you'll get your downloadable games, movies, demos, ect. The PS Store has a ton of demos on it, in addition to plenty of downloadable games. Unfortunately, I can't help you there. I'm not really into that sort of thing, and I perfer disk-based games. However, they had a ton of movies and TV shows on there. Seriously, think of a random movie or show right now, and they probably have it. And while they don't have as many older games as Microsoft has on Xbox Live, they do have a ton of PS1 titles that you can download them if you missed them two generations ago.
That's all off the top of my head, if you have any more questions, just ask away.
Go nuts man, I love the PS3.
