Assuming that you are talking about a video projector (as opposed to a film projector or a slide projector or an opaque projector), the relevant factors are the size and type of the screen and the throw distance.
Throw distance (lens to screen) divided by the width of the screen gives you the "throw ratio," which determines what lens(es) you need for the video projector. If you have a 10' wide screen and a 40' throw distance, then you have a 4:1 throw ratio. A $500 machine will likely have a non-interchangeable lens, so you are stuck with whatever comes with it. You need to make sure that this works for all of your potential uses.
The size of the screen is also relevant as it relates to the brightness that you need to achieve. This is measured in "lumens." Screens have a property called "gain." A standard matte-white screen has a gain of 1.0 and a wide viewing angle. A silver screen has a much higher gain, but the brightness falls off significantly for off-axis. In general, you want the matte-white type. There are intermediate high-gain screens as well, with similarly limited viewing angles. In any case, to meet the cinema standard for brightness (darkened room), with a matte-white 1.0 gain screen, you need 16 lumens per square foot. If your screen is 100 square feet, then you need 1600 lumens of brightness to meet that standard. In reality, you want to double those numbers to account for bulb aging and overly optimistic specifications. You can always make a bright image dimmer, but not the other way around.
There are lots of other factors involved, but those are the basics. If you can find something that meets those specifications and has the inputs that you need, get it.
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