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I don't know Frame [...what did he say?...calls himself a tech writer?]
but I don't think that matters much for the purpose of addressing your
questions.
In general: Think Output.
That should determine the resolution at which you import/capture an
image. As far as I know, it doesn't really matter what your screen
resolution is, if you capture at 96 dpi and then print that out, your
screenshot will look fuzzy as all hell. I don't know what the options
are with the program and file format you are using, but most .jpg
filters will give you a dialog box allowing you to specify your
resolution and the exact size of the image. If you know that your
finished image will be in a 4" wide box (in the printed document, and
you choose 300 (dots per inch) dpi as the resolution, then you can tell
the filter to convert whatever your image is to be 1200 dots wide by
whatever height that works out to be while maintaining the aspect ratio.
Mind you, that will be a somewhat hefty file in terms of memory it takes
up, so maybe you only want 150 dpi. But the lower you go, the more
clarity you sacrifice in the final image.
If your output is a Web site, i.e., intended for on-screen viewing only,
then it makes sense to scale your resolution to 96 dpi, but I would not
use that for a document intended to be printed.
If you are working with a professional print shop, you might want to
give them a call and find out what file formats they are comfortable
working with. Professional printers tend to use PostScript machines,
which means they prefer to use .eps (encapsulated post-script) files for
images. Frame most certainly would support this file type, but I don't
know if your screen-capture utility would export to it. Of course they
can also handle bit-maps, but if you have an established printer, you
should probably discuss with their production people what format to use.
I begin to think that I am probably causing more confusion than any I
might be clearing up, so perhaps I will leave your question to someone
who wants to restrict their answer to the terms you originally framed it
in....