I've got quite a bit of experience with this so hopefully this will help. I started a small business back at the turn of the millennium but the product was a bit bulky for shipping etc. I did put together a web site with much of the information I learned throughout the process here:
It's a couple of years old but most of the information is still relevant. Here are a few thoughts:
If you want a dedicated projector I found the Optoma movietime players to be ideal. (models DV10 and DV 11). They have a built-in DVD player so you don't need to mess with other hookups. You can use the built in speaker for a small group or hook them up to a boombox / stereo etc if you need more volume. I think they're getting hard to find but are still avaialble. Epson has a moviemate that's similar.
If portability is the priority, the Pico projectors are it. They don't throw much light though so you'll want it pretty dark - especially with a big screen.
Any projector will actually work. For a theater application something with a "native" widescreen (16X9) aspect ratio is generally better.
Anything reasonably priced will need it to be beyond dusk for a decent picture. If you want to use it in daylight you're talking about tens of thousands and even then you'll need some shade. Don't get too caught up in the "lumins" BS. Once you have 1000 or more you'll be OK for this purpose since you'll need it ot be dusk anyway. Even a couple hundred will do well when it's truly dark out.
There are really cool prefab screens that work great. A few options are
-The pull-up kind (I sometimes use these in the camper)
-Fixed frame - if you have a wall you can mount it on (e.g. side of the camper)
-Folding frame - these are really cool and portable, but wicked expensive if you buy the prefab ones. If you've seen presentations at conferences they often use these.
DIY. I've found that simple white muslin fabric works very well and is versatile. You can find it in very wide sizes too. One of the primary benefits is that you can use it as front or rear projection so you can hide the projector and other sensitive equipment from scurrying youths. If you really want simple, use black duct tape around the edges (any size but use a 16X9 ratio length to height) and pop some grommets in every foot or so. You can then just bungee it to anything that can be used as a frame. Awning poles are great for this.
In any case - check out the site above and I think you'll get a good idea of what to consider. Our backyard theater is always a big hit, and when we do it at a campground we always meet tons of people. Enjoy!