To achieve a real world contrast of about 12:1 you want no less than 80 lumens per square foot of screen size.
This isn't really a 'cheap' option. Typical screens for boardrooms and home theater typically are 120" diagonal, so you are talking about a screen of nearly twice that area. It will be significantly larger and require more light.
You also need to consider, with rear projection, how much room you actually have and what type of screen you are using. A short throw lens, with a projector with enough light for a screen that size could easily run $20,000+.
Most schools, when building out an auditorium, have a consultant design and specify a proper projection setup and include it as part of the cost. Typically, this is part of a long-term installation and often requires professional installation.
This is not really the list I would use...http://www.projectorcentral.com/projectors.cfm?g=1&hide=0&st=1&mfg=&p=1000-10000&w=&r=&br=8000&br=12000&ll=<g=&t=&db=&dt=&c=&ar=&dvi=&wr=&pjl=0&pjw=0&pjh=0&td=&is=&i=d&oop=1&sort=%24&sz=15
I would only use widescreen projectors, but you should be looking at no less than 8,000 lumens, and expect a price of $5,000+ for this as a starting point.
[Edited by AV_Integrated on Nov 30, 2016 at 6:04 PM]
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