Just got this a few days ago:
Intel Core 2 Duo e6600
4GB OCZ Gold DDR2
ATI x1950xtx 512MB DDR4 (MSI)
My most expensive upgrade ever... by alot. (I had an AthlonXP)
It should handle Bioshock alright

GRAW seems to be pretty easy for it... I played System Shock 2 a couple of years ago, and it was a great mixture of FPS and RPG, Bioshock should be awesome.