I’d contact a true expert like Mr. Size (or someone he recommends) and get great advice. Perhaps he could work from a floor plan.
An amateur’s take on your situation:
1. Get good blinds for the windows. Later on, if you have a nice view, you might invest in ND or CTO+ND filters over the glass, but for now, with your budget, just get rid of the complicating factor of daylight.
2. Go fluorescent for your lighting. Cooler, cheaper in long run.
3. Overhead grids for SAFELY hanging lights would be a big plus, especially for fluoros with their limited throw.
4. Some central control of lighting (either by DMX or by simple on-off switches) would be good — especially a lightboard.
5. You haven’t mentioned audio. If you don’t do major soundproofing you’ll likely have many takes ruined by distracting (“unmotivated”) sounds.
6. Finally, if your budget is too limited to do three rooms well, do one room well and use simpler temporary solutions for the other two.
Paying a real expert would be your best investment. True, your budget is small, but you also have a lot less money to waste on the wrong plan.
Good luck!
bob c