What GPU would bottleneck a Phenom x4 840?

I've been delaying an upgrade from a 1GB DDR3 6670 and the Hynix fire kind of makes me want to upgrade before a potential rise in prices so what would be a good GPU to upgrade to? I'm also considering an APU with the 6670 but a better GPU will probably work better. My budget is around 350$. I basically play all genres and don't care much about anything more than texture quality and FPS if that matters.
System specs:
Phenom II X4 840 CPU, 8GB DDR3 1333MHZ RAM, shitty 400W PSU that I'll likely need to upgrade, mobo ( http://www.ecs.com.tw/ECSWebSite/Product/Product_Detail.aspx?DetailID=1139&MenuID=19&LanID=0)(http://jarcomputers.bg/l_en/?m=7&i=539867&t=0)
It's a prebuilt system.

well this is a bit difficult, because its a pre build and there are some more parts on it that are not that great. like your mobo for example, but i think the best way is to upgrade you system part for part. starting with the GPU is a good idea.

i would go with a Radeon 7950. thease cards are realy great, for a good price. an overclocked 7950, can compete right up with an 7970 GHZ edition, and also with an OC GTX770.

suggestion: Msi 7950 twinfrozer.

grtz Angel ☺