David
Not sure I can add much to help you. As Don has said I currently use a continuous lighting set up with two head - Don has pointed you at the thread where I describe my set up.
I previously used a set up based on battery powered flashes with a Metz CT4 as the main one. To get the diffused soft lighting I would either bounce out of a brolly or shoot through a white one. The problem with flashes designed to work on your camera is the slow recycle time so if going down the flash route I would say a couple of studio heads is essential.
If I was planning to to studio only work I would probably go down the flash route because the power output enables a greater range of f stops and the short flash duration ensures there is no blur due to the subject moving. With continuous lighting even though my units are rated at 500 watts each to get a decent shutter speed ~1/250 I need to use ISO 800 & f4.
I went down the continuous route for photographing babies and kids under the age of ~5 Here I could be taking 100-150 shots in the space of 20-30 minutes or less to produce images like
this or
this
The thought of firing that many flashes in that short space of time might give kids stars before their eyes