I would pick up a Epson projector. LCD projectors tend to have much better and more accurate color at larger screen sizes and higher lumen levels. The DLP models can be 'cheap', but rarely actually can deliver accurate colors.
Sharpness is NOT going to be an issue, as long as you are using Blu-ray. Don't touch DVD, that's 20+ year old technology and isn't high definition.
Contrast is irrelevant in reality. You aren't in a controlled theater space, so you aren't going to achieve more than about 500:1 contrast ratio. Don't worry about it. People watching really won't care.
This is the list to pull from, and there are actually a bunch more beyond Epson who have LCD projectors, and Panasonic, Sony, or NEC are all acceptable as well...https://www.projectorcentral.com/projectors.cfm?g=1&hide=0&st=1&exp1=1&r=16&br=4000-7000&c=&w=&db=&ar=&zr=&wt=<g=&ll=&wr=&dt=1.0
Those are 'new' models, and you can adjust the search to look for used models. I would stick with 1920x1200 resolution as that will work well and is consistent with business class models.
There are some tradeoffs when not using projectors specifically designed for theater use, but unless you are ready to dish out $80,000 it hardly matters.
Plan to spend several thousand dollars at least to get a reasonable image, especially if you are charging to setup and show these movies, there will be an expectation for quality.
NOTHING can be viewed before twilight at the absolute earliest. The later, the better. Projectors need dark spaces to work.
- Theater, whole house audio, and technology consultation during the build and installation process in the Washington, DC metropolitan area.