While scanning - when creating the image, resolution determines the spacing of the pixel samples taken from the original master copy. If we scan a width of 2 inches at 100 dpi, we create an output image width of 200 pixels. This is basically all resolution does, and then the output device takes over.
While on video screen - Scanned resolution no longer has any meaning other than size. The image width of 200 pixels will occupy 200 pixel positions on the screen, which might be 800 or 1024 pixels wide itself.
While printing - Resolution is just a remembered number from the original scan, and now it is used to determine the printed spacing of the pixels on the paper. 200 pixels at 100 dpi will print as 2 inches width, same as the size of the scanned original. We can scale it if desired, and print it at 200 dpi, producing a 1 inch width, or as 50 dpi, producing a 4 inch width.
But the printer obviously will have a preference for some particular resolution number that's best for its dithering capability. 100 dpi may not look good if the printer wants 250 dpi. Meaning, this image may not be of sufficient size for such scaling. We can print larger than we have data pixels, not good. Or we can swamp the printer with a huge image, causing a flood of excessive pixels for which it has no use, not good either.
So, how much resolution for printing?
That's dependent on the capabilities of the output device. You always scan for the output device. There is certainly a maximum useful resolution for printing, and it's MUCH LESS than you might think. Printers vary, some are 300x300, 360x360, 600x600, 720x720, or even 1440x720 now. It sounds like we need to scan at those numbers to match it, but that's NOT how it is. This advertised printer resolution is a different concept than the scanner or video resolution we are used to. The printer resolution is referring to addressability of the ink dot, and NOT the resolution of the image. Several printhead ink dots are required to make one pixel image dot. The printer's image resolution capability is much less than the advertised dpi numbers.
Yeah, so how much resolution?
Have patience my friend, we're almost there, honest, cross my heart. <grin>