You can use continuous lighting for portraiture but unless you want lights bright enough to blind your subject, causing them to squint and their eyes to tear, you will need to work at ISO values above the minimum ISO value of your camera. Typical is ISO 400 or 800. Most camera's can produce perfectly acceptable portraits at these ISO values.
To maximize the amount of light without blinding your subjects large light sources are better than small ones. The Kino Flo lights Peter Hurley used before he brought out his own brand are one example.
You can save a lot of money by making your own long tube fluorescent studio lights. Joe Edelman made his own long before anyone ever heard of Peter Hurley and he was kind enough to make some video tutorials on how you can do it too.
Be sure to watch all the videos. the change to T8 bulbs in the last tutorial is important.
Living and loving it in Bangkok, Thailand. Canon 7D - See the gear list for the rest.