I have a study which I use for a studio. Effective space is about 6x9 feet. Celling hight is only 7.5 feet tall. I usually take portraits (mostly self portraits) in the studio. Walls are white and the ceiling is white as well. Currently using CFL continuous lighting diffused with 43" shoot through umbrellas. Having the greatest difficulty shooting portraits where the background (thunder grey muslin) is 1-2 stops darker than the subject because of light spill. What would be the ideal lighting equipment for this space? Speedlights in a SoftBox? Monolights?
I recently visited a professional photographer to learn some portrait techniques, and he used some black "boards" that he placed up against the white walls to avoid light spill.
The boards were simply long boards of polystyrene painted black (I think they are made for heat insulation purposes). So they are easy to pull out and set up when you need them.
Small rooms make very bad studios. No lights or light modifiers are going to help you much, if the light reaches you subject then it's going to past your subject and bounce off every surface.
Your only hope is to reduce the amount of light bouncing off your walls by covering them with a dark material. You can use velvet or any widely available slightly shiny black material for this purpose, or if you can, get something like this:
The type of light you use has approximately zero effect (unless you're using the CFLs "naked" rather than in a reflector, which will necessarily increase spill). No matter what you use, you need to manage the task of putting light where you want light and not putting light where you don't want light.
Both of the previous answers posted (by Pete and Matt Grum) concentrate on one aspect of the problem you're facing, and that's managing wall/ceiling reflections. Both have suggested using black panels of one sort or another to cut down on those reflections, and that's a valid suggestion. But it's not the only tool at your disposal, either.
The only good things you can say about shoot-through umbrellas is that they are big, portable and (relatively) cheap. And on an exterior location or in a very large space, those are the only things you'd really care about. In a small studio, the downsides far outweigh the good. They reflect more light than they let through, so there's an awful lot of rear spill, and the front surface (when used as a shoot-through) is convex. That does two relatively evil things: it throws light everywhere, and it creates a light source that is significantly closer to the subject at the centre than it is at the edges, so it's not nearly as soft as it could be for the size. Something built along the lines of the Westcott Halo will fix the rear spill issue; something more like the Apollo or Apollo Orb will fix both the rear spill and the convex surface issues. (Note: those are the brand-name items; rip-offs abound at much lower prices. And don't feel guilty about them, since any patents on the basic design would have expired years ago. The Apollo is at least 25 years old, and probably older.) If you can use a brolly and the lights aren't of the "hot" variety, you can use a Halo- or Apollo-type modifier.
That handles the basics of pointing the light. Then there's the whole inverse-square(ish) law thing to take into consideration. Get your lights closer to your subject, and they will be proportionally further from the background (even if that means that the actual distance to the background is smaller). The same goes for reflectors/fill cards: get them in close enough that they're only doing the job you want them to do (and you'll have to bring the reflecctors closer if you bring the lights closer, otherwise you'll get a lot more contrast).
If you need to light someone full-length in a small space, it's far preferable to use a tall light in close than a mid-sized or smaller light at a distance. That can mean something like two or three smallish square softboxes stacked, which is often easier and cheaper to do than a single large strip box, especially if you're using CFLs or speedlights. (Square softboxes are easy to fill with light, but they're the least-handy shape for most lighting. Strips are almost always a better choice. In this case, making a "strip box" out of small, square softboxes that you can easily fill with inexpensive light is a great compromise.) A C-stand with clamps and arms would be the usual way to build the stack, but it's something you can easily DIY for under $50 as well.
Grids, too, will help a lot when it comes to keeping light from winding up where you don't want it. But they can be expensive, or fragile (poor stitching and fabric), or both, so they may not be the best option for you. If the budget is there, though...
Finally, you can flag the light(s) to keep them from directly hitting the background. If the reflections hitting the background are from those very distant walls and ceilings (distant, now that you've brought the lights in tighter), they'll be at a relatively low intensity.
With so much white space around that close to the scene you will never ever be able to control the light in the way you aim for. The white walls act like big but uncontrollable reflectors. So turn the small room into a black box and use some sort of black curtains or carton to darken the wall(s) and ceiling.
The next thing your set would require is space, meaning distance between the sujet and the background. Unfortunately you don't have that. So use barn doors or build your own from black carton (should be cheap in every stationary shop) that shields the key light (the main light source for your model) from falling onto the background. You may want to use separate lights for the background which you need to shield from falling onto the sujet.
And that's basically it. Everything else is up your creativity.
You can achieve all that with one or two torches as well as with an army of the most powerful studio flash lights available. However, as you photograph real humans, those who breathe and blink and always bounce a bit, I'd strongly suggest flash lights. You may go for used or cheap ones but ensure that their power can be reduced in a controlled way up to 1/32th at minimum, preferably 1/64 or 1/128.