You've got a 305W power supply, so I'd probably just throw a Radeon 7750 in there . That's the highest end graphics card you can handle without also upgrading power supply. Your CPU is pretty slow for modern games, so you might need to upgrade that, which would alse require a RAM and MB replacement.
If it were me, I'd start with the 7750 and see how that does. If you still feel like you are lagging, then you'd need to upgrade MB/CPU/RAM as well.
One more options would be to purchase a cheap socket FM2 MicroATX motherboard, an AMD A10 processor and 4GB of DDR3-1866 RAM. That should be about $200 total and you'd get a little more processing power than the above G860+7750 solution, but not as good graphics. AMD A10 have a pretty good build in 3D graphics that rivals a $60 graphics card like the Gt 630 or Radeon 6570.
Look strongly at the HD7770 vs. the HD7750. Much stronger and at 80W TDP will run along with a low power 65W E6400 on a 300W PSU. (I did not cross check twelve25, assumed he got the PSU rating right. The rest of his append was credible).
p.s. your CPU is a core 2 E6400. glad you gave the frequency so I could cross check. This is not a bad CPU. With a decent video card you'll be surprised how much better you can game.
edit: forgot. As you look at video card and CPU upgrades the last pages of the two articles below will let you compare the new parts to what you have. You'll see your current video is hopeless and your current CPU is not great, but ok.