Some basics about lighting:
The smaller the light source, the harsher the light is and the sharper the shadow edges are.
Light modifiers (umbrellas, brollys, softboxes, diffusion panels), are used to make the light source apparently larger. The larger we can make the light source appear, makes the light look softer and it makes the shadow edges more diffuse so they 'wrap'.
So for portraits indoors or outside we usually want as large an apparent light source as we can get as our main light.
High quality portraits are made using as many as 5 lights - main light, fill light, hair light, accent light, and kicker light.
There are 2 main light types - constant lights and strobe lights (flash).
Constant lights are inexpensive, but are short on light power. The power issue boils down to the camera shutter speed.
We have to use a shutter speed of at least 1/100 when we shoot people because people are usually moving a little. 1/100 will almost always stop that little bit of movement.
Constant light power is stated as so many watts of power. One watt (W) is equal to 1 joule per second. The key in that phrase is
per second.
A 100 W constant light delivers 100 W each second, but our camera shutter is set to 1/100 of a second. some 5th geade math so us that 100 W divided by 1/100 = 1 watt being delivered in the 1/100 of a second the shutter is open.
100 W isn't a lot of light and 1 W is 100 times less light.
The more powerful constant lights are, the hotter they get. Rooms, people, and any metal near the lights all get
real hot, real quick when using constant lights. Plus to get enough light to keep the shutter speed short enough, you have to use more powerful lights, which get even hotter.
All of which is why most portrait photographers use Flash, or strobed light. Decent starter studio strobe lights need deliver about 150 watt seconds. Like above, we have to look closely at that sentence. Watt seconds is not the same as watts
per second. 1 watt second is a lot more light than 1 watt per second is.
Strobe lights deliver all of their light in a very short time frame. Camera hot shoe flash units at full power have flash durations in the neiborhood of 1/1000 of a second. Studio strobes are usually a bit slower and are around 1/500 of a second or so.
The short duration of the flash of light can be used to stop that little bit of subject motion instead of the shutter speed doing it. Constant lights are on all the time so they have no motion stopping capability at all.
With the shutter speed freed from the task of stopping motion, we can now use it to control the exposure of the ambient light in the scene we are shooting. Plus we can use the lens aperture and the power output of the strobe light to control the strobed light exposure. None of that is possible when using constant light.
An issue with flash is that we can't see where the shadows will fall until we actually take the shot. Which is why studio type flash units have what is called a 'modeling light'.
A modeling light is a 100 W or 150 W constant light we can turn on and use to see where the shadows will be so we can set up our strobed lights before we release the shutter. Many hot shoe flash units have a modeling light mode that works a bit differently.
In short, to light portraiture, constant lights are inexpensive but have some difficult, if not impossible to over come technical issues - low power and heat.
Strobed lighting is a bit more expensive, but offers many, many technical and environment advantages.
This studio strobe light kit often goes on sale. Check the web site often -
Calumet Genesis 200 2-Light Kit
An almost as good kit is -
Flashpoint 320M Portrait Wedding Monolight Kit, with Two 320 Monolights,9.5' Stands,Umbrellas, Snoot and Carrying Case