Your 350W limit your graphic cards choices. If you upgrade your PSU to 600W atleast (Antec, Seasonic, Corsair), you can put Radeon HD 6950, a beast card. If not, you only limited to Radeon HD 6670, not a beast card.
May i add that a 600/500 wat power supply will be sufficient but at the same time i dont think the current case that you are using will support it.
the power supplies are for a ATX form factor, mid range to big sized
and your case seems to be on the smaller side maybe only having an micro-atx motherboard, ( which is small ). and your case is only 14 inches high while the standard Atx case size is 17-25 inches high.
In the price range indicated, the factory overclocked 6950 and 560 Ti run neck and neck in single card confirations (tiny 11 fps lead for the 560 according to Guru3D)....once paired in CF/SLI however, the 560 Ti dusts the 6950 at 1920 x 1200 by iver 100 fps. However, the new boy arrives on the block in 9 days.....it's a hybrid 560/570 and will be called the 560-448