The 8350 is a good chip but it takes a lot of juice when overclocked. A good 600W unit should be plenty but I wouldn't overclock it on your current PSU, it might take your whole system if it blows up! My advice is to either :
1 - Get the 8350 but don't overclock it until you get a new PSU.
2 - Get a decent 600W+ PSU (The Corsair CX600 is a good cheap option) and you'll be fine overclocking both the 8350 and the 7870 if you get it.
Never cheap out on a PSU!
antec have a good range of cheap but good quality psu's along with corsair. good deals on xfx psu' often come up too.