I'm currently working to book some screenings for a documentary and would like to see if anyone can help with some guidance for projector specs that will produce an adequate display of my film. The film is 1920x1080p 29.9 fps. I realize the venue can play a big role in the display based on room size, lighting, etc. But I'd like to see if there is some fundamental guidance to follow as I contact various venues to determine how well the projection unit a location has will display the movie. I'm promoting the movie with no budget at libraries and other public places so the locations don't normally get questions about the projector image quality.

The movie is available as an mp4 file (1080p or 720p), dvd, and blu-ray if there are suggestions for inexpensive options for me to purchase and bring to the venues.

I think the real answer is throw the best quality 1080p source/low compression codec you have at the projector.
I have a DPI Titan Quad 1080p 3D

Projector Detail (http://www.digitalprojection.com/BrowseProjectors/SeriesList/ProjectorList/ProjectorDetail/tabid/87/ProjectorId/217/MarketTypeId/10/Default.aspx)

that will take anything you can pump through the hdmi connector. but when I put standard def TV signal through the connector it's less sharp and saturated. A good Bluray recording can really make a huge difference in the projected image. Also Hi-Def TV looks much better but now where near as good as bluray..

a simple rule is to have 1000 lumens per meter of horizontal screen.
if the room is dark, you can go with less.
contrast is a different question that can impact quality more than quantity.
the more ambiant light you get , the more contrast you need. To compensate you could use a gray screen instead a white one.
Gain of screen can help if audience is well in front of screen, do not go for very high gain screen (hot spot and narrow view).
DLP is then better thans LCD for this kind of use.