As an owner of the Playstation 3 console, I enjoy giving recommendations to fellow gamers.
As of late, I feel a good start on a gaming library for your console, considering your low budget, would be to either purchase bargain games such as:
-Uncharted
-MGS4
-Motorstorm
-Ratchet and Clank: Tools of Destruction
-Killzone
-Infamous
-LittleBigPlanet
-Rock Band 2 (If you include the whole set, be prepared to cough up some cash, otherwise purchase a guitar only)
-God of War Collection
-Resistance:Fall of Man
These games can be usually found on-the-cheap at local retailers. Among those recommendations, your friend recommended Red Dead Redemption and as I've heard, it is a great game. Although fairly new, it would be a game worth purchasing. Another fairly new game worth purchasing is Heavy Rain. I've only been hearing good things about this game, so you should look into it.
Not only are those recommendations well rounded, popular games, but should provide a satisfactory experience. The great thing about the older games are that they are cheaper and serve as gateways to the entire line-up in that series. Don't worry about having an older game. Just know that you have something to start with.
Be sure to look into online play from still going games such as Rock Band 2, LittleBigPlanet, Resistance 2, Warhawk, Burnout Paradise, MAG, GTAIV, and Street Fighter IV.
-Playstation Store-
While I recommend disc based content, how about you look into the Playstation Store? The Store has enough content to garner your attention because it has downloadable content through online purchases, and many of the games are cheaper than regular disc-based content (Not including Add-Ons such as expansion packs), and includes Playstation One Classics, such as Resident Evil, Silent Hill, Crash Bandicoot, Final Fantasy, and others. There is also original and exclusive PSN titles, as well as add ons for disc and non-disc based content. For example, you can find Rock Band 2 songs for purchase and play, or a slew of LittleBigPlanet add-on content for further gameplay options. Get creative! But more importantly, get it cheap.
Really, if you look into the Playstation Store, you get a good idea of what games are out there. I highly recommend looking into the Playstation Network.