The room is about 3 metres wide and 6 metres long. I would imagine it would be used mainly for Movies although i guess we would at some times use it for gaming. Theres quite a bit of light coming in, from french doors etc.
I would recomend something like the Epson EH-TW6100 as its very bright and will help combat the ambient light. I have the previous model with a 92" screen and its brilliant and has decent 3D to boot.Both the PJ and screen will come well within your budget.
This is a larger version of my screen HERE and pictures of my setup are HERE