There is hardly any difference between a 650W PSU and a 700W PSU.. The extra 50W may account of 4A at max.. Mention the brand and model of your current PSU.. Your proposed system spec can easily be powered by a good 550W PSU (such as the Corsair VX 550W)..
My brother's i7 920 @ 3.7ghz, 6GB of 1600mhz 1.65v memory, and 5870 pulls about 350watts at the wall under full load(CPU+GPU at full tilt). When he plays games, his cpu is nearly idle, so it rarely every even gets up that high.
All the good PSUs are in the 650-850 range now-a-days, so some name brand in that range will be fine.
Choosing a PSU should not be left to guess work.. It is one of the most (probably THE most) critical component while building/choosing a system.. The risk gets higher when you are not sure about the branding also.. Can you provide the technical specs of the PSU.?
It may not be the case but 'Standard' sounds like generic to me.. Till someone more knowledgable in this scenario finds out some better technical information, my recommendation is to get a better known brand PSU..