The second place I airbrushed (and the set up I suggest for you) was in a rented house. Again, I was fortunate enough to have a dedicated hobby room (2, in fact), but the system would work for any apartment or whatever. I built my own extractor unit, which, while not pretty, kept the room immaculately clean. I know this because, again, when it came to mega-souji before we moved out, the room was clean as a whistle. What I did was:
I bought a kitchen wall extractor fan from K's denki. It cost a few thousand yen. These are the fans you see in kitchen walls for sucking out oily cooking fumes and suchlike. It was about a foot square, and 3 or 4 inches deep. Using cheap, thin plywood (bought from the hardware store for about 1000yen for a huuuuge 2m x 1m piece) I built a trapezoidal shaped extractor hood with a bit sticking out the back that fit as closely as I could get it to around the fan casing. This whole assembly was perched in an open window. I made sure to protect the window frame and desk surface with some newspaper, and closed the curtain over the top of the hood to ensure all air-suck was through the hood. et voila - an extractor unit that you can put up and take away in less than a minute.
The final extractor option is to get a 35 year mortgage and build an entire house and custom designed room around your extractor fan of choice. This is what I have now, but I wouldn't necessarily recommend it

Anyway, I really really think an airbrush would be very helpful to you. It's a really useful tool. It aint a miracle worker, and it will not, contrary to popular belief, allow you to paint entire armies in no time, but it will allow you to get a lot of tanks base coated very fast, and also do cool shit like zenithal highlighting, weathering (this is FUN!) and camo markings really easily and with minimal fuss.
I'll see if I can find any pics of my extractor hood from my previous place. I'm pretty sure I have some somewhere. If I find em, I'll edit them in here.
*edit* meh, not the best pic, but you can see the booth on the left, atop the desk. You can see it's just a few bits of wood (stuck together with glue when doable, masking tape and a wee hinge where an angle was necessary), on top of another (separate) piece of wood on a desk. It actually sticks out of the window by a couple of inches, and the fan unit sits neatly on the window sill.

and some da-vinci-esque works of art to perhaps illustrate what I did...


Hope that helps

* You'll find that airbrush paint is very powdery if you get it on anything except the mini you're painting. It brushes right off with a fingertip. The reason for this is that it's a very fine mist when it comes out the brush nozzle. As long as it hits a surface close to the nozzle (i.e. your mini) it will still be wet, and therefore stick to it, creating a layer of paint. However, if it doesnt hit anything it'll kinda fly off into the void. Being so small and finely misted means it dries out into a fine powder within a second or so. Thus, your room doesnt get covered in paint - it gets covered in fine powder. This is why we wear dust masks when airbrushing

*edit* oooooor, you could just buy a spray booth. Whatever suits best
