Nooooo!!!! don't listen to him, your gonna F*** you machine up, that Power Supply is weak... Doubt youd be able to run much of anything on it. Try more of a card that doesnt require anymore power than what it gets off the PCI express slot. like a GT 430 or a 7750.. the Low end 600 series will be out soon if you can wait...
But do not buy anything above that unless you get a new power supply. That power supply only has 375 watts? I would just get a new PSU just to up the insurance policy on your system than worry about graphics
1st upgrade your PSU, then think about a GPU. Its kinda harsh see in that way but is dangerous having a non-certified PSU with that low power. You should know that by time, the efficiency of PSU dregrades over time, it wont be delivering 375W by now.The 7750 for now is your best bet. When you upgrade to a new rig you throw on it a good GPU and also get beefy PSU to handle it and new upgrades over time.
Im kinda surprise that you PSU could handle an old Quad core, 2 HDD, and a 8600gt, which all the components uses good amount of power.