Matt's right. Get flash!
Continuous lights are hot lights. Minimum for portraits would be 3x 500Watts = 1,500Watts. That is a lot of heat! Very inconvenient in confined spaces. And a fire hazard!
(And can your home's electrical system support that kind of drain?)
I have a 'portable studio'. It basically consists of 3 wireless 5600D flashguns on tripods, a 3' and a 4' silver/white reflector. Gives me plenty 'oomph' and endlessly variable possibilities, including faking 'softboxes' and balancing shadows. Easily fits a medium-sized suitcase.
When working with live subjects I mostly use the camera unsupported. Flash freezes motion anyway, and it keeps me much 'free-er' to move around, direct the scene, try different viewpoints and angles, and/or adjust the light.
I submit a 'portable studio' like this is much more flexible than a fixed continuous studio light set and is therefore used much more often. Like on location!
The downside is that you have no modelling light. But hey! this is the digital age so you just do a test shot and look whether you like the light setup as is.