i would definitely be bringing it inside when not in use... i am thinking some kind of tripod mount... and the screen would also be a temporary solution... something that could be taken down and stored in the garage or something....
With that in mind, you really need to shoot for a target size and a real world expectation.
If you intend to show no HDTV and just some DVDs (not Blu-ray) and quality really isn't that important to you overall - but needs to be reasonably acceptable. The cheap business class XGA monitors will deliver decent brightness and a decent image. Don't expect a lot in the way of smooth motion handling, or superior black levels, etc. But, for an image that 'works' the price is hard to beat.
BenQ puts some refurb units up on their site which aren't bad for home theater and the price is very good:
http://shop.benq.us/benq-us/searchresults.aspx?dept_id=21&culture=en-US
Specifcally:
http://shop.benq.us/benq-us/product.aspx?sku=3591737§ion_id=566&culture=en-US
You get 720P HD projection w/HDMI connectivity.
One of the big lacks of the XGA cheapie business class projectors is that they most often won't have a HDMI (or any digital) input, and likely don't have a direct component video input.
This BenQ model will fill a 120" screen after dark without issue.
For a screen - you have a ton of DIY options which work.
I've made a screen from a sheet twice. I use one version for front projection outdoors and one for rear projection in my garage on Haloween. It is passible, but not really very good overall. Still, it is fun.
Better is going with black out cloth or one of the DIY options from AVS Forum which are extensive.
For FAR more ideas than even I can come up with, you definitely want to look at:
http://www.backyardtheater.com/
Have fun with it all! Oh, and don't forget the audio.