Ok, since you won't be here teaching English or something along those lines you probably will be looking for a higher standard of accomodation. That's why I emphasized "at least" in my apartment rental estimate. A good online service is
www.oferty.net -- but it's all in Polish. As far as i know, there are no online real estate portals in English (besides the ones from the agencies). There are no houses in the center of Warsaw, only apartments - houses anywhere near the center are
very expensive (at least 8000 zloty per month).
I have no idea how much a rental car would cost (we have all the major companies so maybe on their website?) but gasoline is about 4.50 zloty per liter.