Hi Boece,
Yes, the projector and Mac Mini and 5.1 sound system will be our home theater. The projector I'm looking at is the InFocus X10:
http://www.infocus.com/Products/Projectors/X10.aspx
Its native resolution is 1080p. If you look at the technical specs, it mentions VGA under the data compatibility: "VGA (640x480)". This leads me to believe that if I plug the Mac Mini's VGA into the projector's VGA, then all I'll get is 640x480. That's really low, so maybe I'm misunderstanding something.
Meanwhile, the Mac Mini offers "DVI video output to support digital resolutions up to 1920 by 1200 pixels." And the projector says it has a DVI input ("requires M1 to DVI cable"). So, that indicates that some high-res connection can happen between the Mac and the projector. But I'm trying to confirm that for sure.
Thanks for your help.