For TV, probably 3:1 screen widths (not diagonal measurement). So for a 65inch 65/1.15*3/12= 14 feet. You might be able to push that up to 4:1 for regular TV. For home theater, collapse that to 1.5-2.0 screen widths. 65/1.15*1.5/12= 7 feet. To sit farther away will pretty much require front projection. There are a lot of good digital projectors from $800-2000, check the AVS forums.
