Oooh, Bestec. Some of their units have real problems, including spiking mobos through the +5VSB every time they are turned on.
I tried to search for that model, but didn't find it; the closest matches were either 250W or 300W, and neither had enough power for even a HD6670. I don't think you should get anything stronger than a HD6570 unless you are also willing to replace the PSU. A quality modern PSU has full range active PFC (no little voltage switch) and some level of 80+ certification for efficiency. Seasonic, Antec, Corsair, XFX, and Enermax/LEPA are among the better brands. I'm not sure how available those would be to you. FSP also has some decent models. Avoid Coolermaster and anything else with a little voltage switch on it. Even a 380W Antec Earthwatts or 400W Corsair Builder (both in the $35-$45 range here, depending on deals) would be excellent choices, able to power a considerably stronger card if desired.