After trial & error I seem to be using 1/80 to 1/125 for indoor flash pictures, any more and you need to bump up the ISO to somewhat compensate for the quick shutter. (ie: dark background)
Although I really don't have many problems with 1/40 which the camera in AUTO mode seems to prefer. (which I believe is the #1 reason for the unwanted blur some people have)
Or if you want more "ambiance" you can slow down the shutter even more, but you'll need a tripod or table.