Projecting the same image size from different distances by using the lens zoom. The zoom effects brightness and to a lesser extent contrast. To calculate the effect on brightness you use the lens f numbers. (f1/f2)squared. For example a projector listed as having a f2.6-2.4 lens works out as (f2.4 largest image / f2.6 smallest image) squared = 85.2. 100 - 85.2 = 14.8% loss of light, largest image 100%,smallest image 85.2%. The effect on contrast is the opposite way round it is higher in the smallest image, and the difference is typically a lot less than the difference in light output, so in this example I would guess about 7% or less difference in contrast. . Since contrast usually has a bigger effect on perceived picture quality than brightness, as long as the image is bright enough, it is usually best to project the smallest image.
Depending on lens quality the smallest image will also usually be sharper than the largest image, but with some projectors the middle of the focus range may give the sharpest image. To determine lens focus and sharpness you want an image of white lines on a black background and face inches from the screen look for the least chromatic aberration (the white does not go sharply into black, but has a colored edge) at the extremes of the screen, or with DLP projectors how sharp the individual pixel structure looks, with DLP you can usually make out the dimple contour in the middle of each pixel.
You also need to take into account the projector offset, the angle its lens aims at the center of the screen. DLP projectors normally have no adjustable up/down lens shift, while some LCD projectors do which greatly improves placement flexibility. Offset is given is a percentage of the screen height that the projector (center of lens) must be mounted from the furthest vertical point of the screen. For example a fixed offset of 136% percent with a screen 62.4" in height, means that this projector would need to be mounted 84.86" above the bottom of the screen for a ceiling mount. 136% * 62.4" = 1.36 * 62.4" = 84.86". DLP projectors sometimes have virtual lens shift to improve placement flexibility but this works by reducing the size and resolution of the image, so is best avoided.
Dlp projectors usually do not have any left/right lens shift, while LCD projectors often do, again greatly increasing placement flexibility. You need to check the lens-screen is absolutely square on, to the screen to prevent key stoning. To check this measure the size of the image top and bottom should be the same length, left and right sides should be the same length. Projectors have digital keystone correction to compensate for not being square on, but this again works by slightly reducing the image size and resolution so for best picture quality it better to not use it.