You have two separate lighting tasks: the backdrop, and the subject. Trying to have one set of lights do both is possible, but more tricky, with more chance you'll regret the results.
For the backdrop, you need soft light; the cheapest thing that will work for your tight space and budget here would be fluorescent tube shop lights, oriented vertically, and washing across the backdrop. It's better if you use tubes with a high CRI rating, but not critical for just lighting the green screen. You can kludge together a mounting system to put these on stands, using for example those spring-loaded clamps used to hold a broom or mop up against the wall.
For lighting the face/head, a soft white LED bulb in a plain reflector housing like this:
with some proper diffusion gel (Roscolux, "tough opal" or "tough frost" available by the sheet from places like Markertek and ebay)
and "barn doors" made of black cinefoil (Markertek again, or amazon)
...will get you striking results on a pauper's budget. Make three: two for the key and fill, one for a backlight, without the diffusion.
A variation on those lights would be to use halogen, dimmable bulbs for the key and fill, and attach "squeezers" or dimmers to them, to control their output a bit. I use Router motor speed controls from Harbor Freight as my "squeezers", because they're cheap, rugged, and already assembled into a usable form.