They over state the power supply requirements due to the increasing amounts of those crappy power supplies that are overrated. I myself have the HD 7770 and it worked fine for my old Antec VP-450 and my Corsair CX-430.
Say I get a 400 watt standard(im assuming they mean ibuypower brand or other generic psu on their configurations) since they didn't specify anything. Would that be good or bad, bad being needing to be replaced.
I believe ibuypower uses Xtremegear power supplies which are kind of garbage. For a system needing something like 400 watts they shove a 700 watt power supply. Honestly, I stay away from such power supplies including bundled power supplies with computer cases like those cooler master cases.
Chances are it wont work if its a 400 watt generic power supply. I mean if it was 700 watts and generic it most likely is around 500 watts (since they over state the wattage). Still no harm done in trying to turn it on with that power supply, but I would advise you to get a new *quality* power supply asap.