There are a lot of very nice people here who will tell you all sorts of ways to achieve a lighing system. And as Thomas has suggested light is light. That, and what everyone here tells you is sincere and will be helpful.
What I'm going to tell you is what you are probably going to need to get yourself into any kind of situation where you can get to be professional at this. This is all bare bones and in my opinion what it will take to get you started. I have been exactly where you are and know what you are trying to achieve. One problem with some of the ideas presented is that you will find it easier to achieve duplicatable controlled lighting with "professional lights" with modelling lights, than with any other system. So by all means use their ideas but if you are serious about doing this for a living you will eventually have to buy what I'm suggesting. All these things are available used and on ebay for hugely discounted prices from what you will see in new catalogs.
You will need:
A monolight (self contained strobe) with modeling light (minimum about 600 watt seconds) examples Photogenic, Alien Bees Calumet etc
A softbox for the monolight (about medium size)
A stand for the monolight
A piece of fomecore for a reflector
A stand for the reflector
A light meter/flash meter
A muslin background and a background holder
The reasons are as follows,
Monolight vs power pack and strobes - both work well but for one light to start with I would suggest a single monolight.
Softbox vs umbrella - both work but the softbox has the ability to control the light better.
Obviously there are many ways to go on this but if you spend the money on experimental jerry rigged systems you could have put the money towards equipment that you could use professionally for years.