If you want multiplayer, stick with the PC (even if your current rig can't play games, you can build something for around the same cost as an xbox 360 elite that will comfortably play all current gen games on reasonably high settings).
If your heart is set on a console, it depends. I have both, and I play the PS3 a lot more (at least lately). Both consoles have pretty good pros and debilitating cons. The PS3 is hard to port too, and as such there are sometimes visual glitches and general problems with multiplatform games where the xbox runs them fine (there are a few select titles that were made for the ps3 and ported to the xbox, in those cases the trend is reversed). I find the PS3 controller to be terrible (it was good when I was ~12, but my hands outgrew it years ago). Xbox live is a joke, I've actually had more sucess with PSN (in that I don't get matchmade to dial up connections somewhere across the ocean every second game) so I guess if you want online multiplayer, I'd be shying away from the xbox. The xbox also tends to have better graphics, the graphics processers are a whole generation newer than the playstations and the xbox upscales to 1080p (where the ps3 just runs most games at their native 720p), so things tend to look slightly better on the xbox (not always, but as a rule, PS3 exclusives tend to have a lot of work put into them and often look better than comparable xbox games simply because of committed developers). The peripherals for the xbox 360 are a joke, they cost stupid amounts of money (hard drives, wireless connections etc), if you want any of those be prepared to fork out buckets of cash. The PS3 comes with playTV nowadays, which is a cool feature (lets you play and record TV), that's probably worth considering if you don't have a hard disk recording system.
Overally, I'd recommend the PS3 as it seems to be better value than the xbox 360 right now. While the game library is far smaller, it has more exclusives that I'm interested in playing. Basicially, buy whatever systems exclusives appeal to you most, if you want to play god of war, demon's souls or metal gear solid 4 go for the playstation, if you're more into halo, fable or gears of war it's the xbox.