There are three basic light type options, hot lights, flash guns and studio strobes.
Hot lights are cheap, but often not well color-balanced, hot and continuous. The only advantage they have other than price is that what you see is what you get. The heat can be a fire hazard, injury hazard and their continuous nature will give you smaller pupils on your subjects- that can be a major disadvantage in portraiture. It's difficult to modify the light because of the heat. More importantly, you can generally only use distance to vary intensity- not a great thing because if you want softer light you have to go closer so your light doesn't become a point source, but if you want less and softer light you're pretty-much stuck. I'd go with full spectrum florescents and deal with white balance issues before I'd go to shop-type hot lights.
Flash guns are relatively cheap, but will require triggers for multiple lights, and don't have modeling lights- for me, the lack of modeling lights is the biggest problem, as you can't see where reflections are, and you can't get a great idea of where the lights will center. You can get small modifiers for flash guns, but not larger ones- that may be an issue for some subjects or lighting situations, but their portability is excellent.
Studio strobes come in two types, pack-and-head systems, and monolights. Pack and head systems have a central AC power pack all the lights plug into, and monolights have their own power source, so each head needs to plug in. I have one of each type. My pack and head system is way too powerful for a small studio, as it's only got three power settings. My monolights are very adjustable, giving me much more control over the light. Both of my systems have modeling lights that track the power settings, so you can get an idea of the overall lighting ratio- I'd always advise against purchasing strobes that don't have modeling lights- you can always turn them off- but you can't use what's not there. You can have good pupil sizes by shooting with the modeling lights on, or ultra-large pupils by shooting with them off.
Monolights are heavier than the heads on pack and head systems, so you have to be more careful with your stands, but these days I'd only take the pack system somewhere if I really needed the extra power, but wasn't getting enough to purchase a couple of AB1600's.
I was doing a product shoot yesterday, and using the modeling lights to get the same overall lighting position for the product in a large warehouse environment meant that I was able to match the previous product shots lighting direction and intensity in seconds with enough power to light up the back of the warehouse and give some good subject separation. With just three AB-800s I was able to nail what would have taken at least six flash guns. Getting the light intensity right with hot lights would have been difficult given the ambient light, but the AB-800's overpowered the shadows from air ducts and loading dock doors enough that they didn't effect the outcome at all. I did use a Vagabond II battery pack with my backlight so that I didn't have to run yet another extension cord from the far side of the section of warehouse I was using for the shoot. The only disadvantage of the Vagabond is that you can't really use the modeling lamps, as they drain the battery too quickly.
For location work, you have to do one extra trip from the vehicle for strobes vs. flash guns, but the extra light power and ability to use larger modifiers make that well worth it for the types of things I do, and it's not really a deal killer for on-location portraits either (If I did more in terms of packaging, I'm sure I could cut out the extra trip.)
I highly recommend getting a copy of Light: Science and Magic as well.
