Look for a thread where someone is asking for the brightest cheap projector for outdoor/late evening use.
Maybe something like the Optoma MovieTIme.. It is 1000 lumens and 480p native (same as the wii) and has a built in DVD player.. so if you are moving it around you only have to worry about moving one thing. It is <£500 new.
I do not own one, so I cant guarantee it will work with the wii, but it seems to do everything you want, you will need to do some research, here is a good place to start:
http://www.projectorcentral.com/opto...etime_dv10.htm