Well, both consoles are great, but I definitely suggest a 360 because of it's online and popularity!
I'll tell you the differences between these two consoles as the PS3 and 360 are slightly identical:
-The 360 can only play DVD's while the PS3 can play both DVD's and Blu-Ray. (Who cares! You want games, not movies)
-The PS3 has free online while the 360 doesn't not. But I have heard that that XBL is better than PSN, even though XBL costs money. Must be because XBL has minimal lag.
-The PS3 will have an Internet Browser while the 360 does not. (You already got a PC!)
-The PS3 has more exclusives than the 360. (Ratchet & Clank, Resistance, Uncharted and more...)
-The 360 has more popularity and sold more systems than the PS3. (Your friends will even own one, I think...)
-The 360 will have Project Natal coming out. It's similar to Sony's Eye-Toy, but it'll be A LOT better!
If you're a strong gamer that will play for hours in a row, then buy a 360 because you'll enjoy the online experience (Even though it's not free), and the gameplay. XBL doesn't lag as much and it's really fun! Just watch out for any annoying kids on XBL (But don't get scared, you'll probably find some mature kids though). If you're an old kid or a teenager, then this is for you!
If you're a casual person that usually loves relaxing while listening to music, browsing the net and watching DVD's a lot, then buy a PS3. The PSN will be worse than XBL, even if it's free, because it has less popularity and it has a good chance of lagging if you have a crap connection. So if you're a adult, then this is for you!
Also, don't believe the RROD stuff that happens on your 360. Because the 360's that Microsoft are selling in the market now has a low faliure rate. That's why people are saying, "PS3 FTW!!!" or "PS3 IS DA BOMB!!1" or "ps3 rules".
Here are the games I recommend you should start with (Well, you don't have to):
If you buy a 360:
Halo 3
GTA IV
Gears of War
Mass Effect
BioShock
If you buy a PS3:
Resistance: Fall of Man
Ratchet and Clank: Tools of Destruction
Uncharted
inFamous
MGS 4: Guns of the Patriots
Now, before you go and buy a console and you don't know which, research these games and consoles and find out which is the best!
Also, if you're buying a 360, buy an Elite because it'll deliver a better gaming experience (120GB HDD, bundled HDMI cables (Unless you got a HDTV), headset etc.) unlike the Arcade (256MB memory card). For PS3, if you buy one, buy a HDMI cable, as the console won't have a HDMI cable included with it (If you have a HDTV).
But, in my opinion, I suggest you buy an Xbox 360. It's a lot better than PS3.
I'm sorry this is long, happy gaming.