Tyler,
A LOT of fine portraiture has been made with a single light source, and I think this is where you should begin. $150 won't go terribly far, but it will get you started with the following basics:
* A nice backdrop. This is something you could make yourself by painting a large piece of canvas or muslin. Unless you're doing really tight headshots, the backdrop is a significant visual element of the portrait and can enhance, or spoil the impact of the portrait.
* A tungsten light source, AKA a hot-light. I would look at a Lowel Tota light, preferably used. These lights sell for less than $150 new, so I bet you can find a used setup for significantly less.
* A light stand and light modifier, probably an umbrella for flexibility and economy. The light stand may come with the light, or a kit such as
this one: For the money, umbrellas are probably the most useful and versatile light modifiers you can get, and they are very portable as well. The size of the umbrella is a personal choice, but remember the larger the umbrella, the softer you will be able to make the light, and it's easier I think to start lighting using a soft light source.
* A reflector, such as a large piece of foamcore or light fabric.
With the above setup, you have a few limitations and many possibilites. You will be limited, as other posters have mentioned, to tungsten film or B&W. And some subjects do find hotlights uncomfortable (perhaps no more than the harsh pulse of a strobe...). The strong advantage of hotlights is that you can easily see the effect of your light placement. For some ideas as to what you can accomplish with a single light source, the following links may help:
Timothy Greenfield-Sanders
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Irving Penn
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Good luck!