You have a good budget, but there are some potential issues.
Flexibility from a projector is like flexibility in a camera. You don't get it without getting a lot of different lenses, and a single camera lens could run $1000+ per lens. Plus the camera. So, a lot of your budget could be eaten up by the amount of versatility you demand.
You also want to figure out screen size. HD projectors are 16:9 aspect ratio. So, 8' wide by 4.5' tall is typical (110" diagonal).
4:3 is another common ratio, but outdated. There are some 'cheaper' models you can get in this ratio that may work well and save you some cash, but they aren't going to match up with modern computers and graphics as well. So, 4' wide by 3' tall, or 6' wide by 4.5' tall.
I really think this is the list I would be looking at...http://www.projectorcentral.com/projectors.cfm?g=1&hide=0&st=1&mfg=&p=300&p=2500&w=&r=&br=&ll=<g=&t=&db=&dt=&c=&ar=&dvi=&wr=&ol=1&pjl=0&pjw=0&pjh=0&td=&is=&i=d&tr=&oop=1&sort=%24&sz=15
I am a huge fan of Panasonic projectors, but the Vivitek models at the top of the list are a really great value. Their lenses are pricey.
Panasonic offers more lens options, but once again, they are pricey.
LED curtains/walls are certainly pricey, but have much better brightness overall and are extremely visible. You pay through the nose to get that brightness.
I would speak to a local A/V company if you can as this type of endeavor takes a great deal of planning to put together properly.
Oh - and almost all projectors can do rear projection. That's a non-issue.
- Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.