If your top budget is top at £300 do whatever you can to extend it so that you can afford a Optoma Hd70 or Hd65....
TRUST ME, do not bother getting a projector that is not Hd Ready in terms of its native display is not true 720p,,,, it will just look awful, I've been there and done it, there really is no point in having a big screen and the image blurry all because a it isn't a HD projector....
The xbox 360 would just be rubbish, its a HD console, so give it a HD display, it will look amazing, for £350-£400 the quality of the projected image is fantastic value for money...
I bought a typical cheap projector first, it was ok to begin with, but very quickly I just hated the image and would rather go to a small tv just so I could see things clearly.
Normal Sky (non-hd) isn't the greatest quality anyway.... so to blast that up in size on a non-hd ready projector.....welll.....
I now have a Sanyo Z5 Hd projector and I love it, amazing clear images on the 360, ps3/bluray film but a big screen at the same time!!
my setup with screens - (360):
Dal's Setup
Trust these guys on here, they know what they are talking about! - Your budget is almost there