Okay, here's a few recommendations:
WIPEOUT HD.
Let me say that again. WIPEOUT! FUCKING! HD!
It should, by law, come pre-installed on every PS3. The Red Ring of Death is probably caused by a 360 seeing a screenshot, realising it will never feel the sweet, sensual caress of this game or its better-than-sex Fury expansion pack and committing suicide.
And yes, you must get Fury as well. It's not an Expansion Pack, it's a sequal. It doubles the number of tracks, doubles the number of game modes, gives an extra (and better) ship for each class with at least two alternate skins unlockable as you progress, and it simply is not possible to get tired of Eliminator.
Next game we shall consider;
KILLZONE 2.
I really like Killzone 2. It is not perfect, but it's damn close. In truth, the problems I have with Killzone are as much to do with the players as the game. The single-player story should be twice as long and doesn't so much end as stop, and Rico is such a **** that the genocide of his entire ethnicity is morally justified in the eyes of everyone who has played this game (including members of said ethnicity themselves).
On the multiplayer front, the only issues you are likely to have is that at lower-levels you can't use all the awesome badges and shit, and on higher levels you STILL can't use the awesome badges and shit because some fucking loser has Spot & Mark and his friends are all playing the Assault Class. Ban these fucking cheap Classes, however, and you'll be left with a truly frantic and fucking brilliant multiplayer experience that will give hours and hours of enjoyment.
Overall, Killzone 2 is ESSENTIAL for anyone who falls into the crowd of insufferable cuntbags who think Call of Duty 4 is the be-all and end-all of gaming, if only so they can be proven wrong. For everyone else, it's a damn fine game regardless.
RESISTANCE:
The Resistance Series I shall consider together, since they're cheap enough to get both.
Resistance: Fall of Man was never much of a looker and just looks more dated with every passing year. This is a shame because underneath the rather poor visuals and a what-the-fuck control system is a gripping storyline and a genuinely likeable cast... except for Nathan Generic-Dumbass-Yank Hale, your character. The setting is awesome because it's Britain and it is not possible to hate a game that involves murdering your way through Grimsby, descecrating Manchester Cathedral and running Hybrids over in Cheddar Gorge (yes, it is where cheddar comes from).
Resistance 2 did a lot to improve the gameplay and made a bloody big leap in graphics, but at a cost to storyline and a few other key points. The first casualty of the sequal was the unique Hybrid-health system - a combination of DooM Medikits and Halo's "Don't get shot for 1.5 seconds" regen. This time Insomniac got lazy and just ripped off Halo. They also ripped off Halo by limiting us to two weapons at a time and making every main character a fucking Space Marine that nobody gives a shit about.
Even so, Resistance 2 makes up for it with the gaming experience. Co-Op is a totally distinct and very fun game that explores the backstory of the setting and what went on between the two games. Competitive mode is great in theory, but when trying to play with a group of friends it tends to fuck up. Team-balancing seems an alien concept with Team Deathmatches being set up as 5-vs-25 and then crashing due to 'not enough players'. The Expansion Pack contains some of the best maps I've seen in this kind of FPS, which is a shame because NO FUCKER USES THEM! Since their release, I have had ONE game that was full. Most are 1 vs 1. If that.
Despite certain issues, Resistance 2 is still very enjoyable and for those who are more interested in plot than mindless shooting the original is a must-have. Get them both.
LITTLEBIGPLANET.
I really shouldn't need to say anything more.