Well, on my old PC I had a 9400 GT, which is around the same performace as your GPU. And my CPU was AMD Athlon 64 x2 dual core 3600+(Which I think is around the same performance level, too).
I could run most of the today games, just at the lowest settings and 1680x1050 resolution, though in some games the resolution had to be turned down to 720p. But there were some games like Skyrim which even run at medium and 1680x1050.
Then I bought a HD 6670(around 80$) And the gaming performance increased drastically. Now I was looking at 168http://www.tomshardware.co.uk/forum/edit/response/119717080x1050 and mostly medium/high settings, even though my CPU was bottlenecking. Skyrim even run at 30-70fps and max settings, with no AA. Battlefield3 and Sleeping Dogs still sucked though 1680 resolution and low settings for around 30fps. But still mostly all the games were playable.
So if you can afford to spend a little cash for the HD 6670 you're looking at much better settings. And you can probably not worry about your PSU, as even my 350W fortron PSU could handle my setup fine.