The useful way to think of video resolution is that our screens show a specific area of pixels, which is adjustable to be 800x600 pixels or 1024x768 pixels, and other sizes too. Therefore, to fit an image onto this screen area, the only number that is important to describe video images is the X by Y image size in pixels, like say 400x300 pixels. For video screens, it is unimportant if that 400x300 pixel image was scanned at 72 or 972 ppi, if the original areas were such that the screen dimensions come out 400x300 pixels either way. This is very simple.
On the screen, resolution determines image size, not quality (printing is the opposite).
The scan resolution is your choice, and it determines the image size created (in pixels), from whatever content you want to show in that image. But once the image is created, all that is important to the video system is the "X by Y" image size in pixels. Knowing this image size, we can judge how much of our screen it will fill.
A 400x300 pixel image will always fill 400x300 pixels on any screen, but this same image will look larger on a 640x480 pixel screen (will fill more of the 640x480 pixels) than on an 800x600 pixel screen. It will be smaller yet on a 1024x764 pixel screen (400x300 will fill less of the 1024x768 pixels). Larger or smaller meaning that it fills more or less of the total screen area, but it is always 400x300 pixels on any screen. The percentage of "fullness" of image size varies with screen size. Don't let this be hard.
If we intend to scan a 0.5 inch width and want to create an image with 1000 pixel width, then we need to scan at (1000 pixels / 0.5 inch) = 2000 dpi (good luck, this is quite extreme, unless we are scanning film). Or if we will scan an 8 inch width and need an image with 400 pixels of width, then we scan at (400 pixels / 8 inches) = 50 dpi. Remember that "dpi" is Dots Per Inch, meaning pixels per inch.
It's still a hard question however. What size do we want? Are we scanning to fill a quarter of a 640x480 pixel screen, or to totally fill a 1280x1024 pixel screen? Only you can answer questions about your purpose.
But if scanning for the web, keep in mind that a few of us still use 800x600 pixel screens, whether you do or not. So, it is a very good idea to switch to 800x600 pixels (or at least to 1024x768 pixels) and check your own web pages (design your web pages to float to adapt to any video resolution).
I hope everyone will always test for themselves the various ideas about getting better results. For example, speaking of tiny images, some suggest images are made better by scanning larger and resampling smaller to get the reduced size. Like the high resolution can somehow be retained when we discard the excess pixels? No, it doesn't work that way. But yes, in moderation, this can in fact sometimes help, in some cases (not because resampling smaller helps, that only discards pixels, but because the photo editor can probably do that resample better than the scanner can). If we want 16 dpi size for a small thumbnail image of a large book cover, then scanning at 50 dpi and resampling to 1/3 size is reasonable for reasons concerning resampling. The scanner may not be as good at such drastic reductions (from 1200 dpi to 16 dpi). But scanning at 300 dpi for the only purpose to be able to intentionally do an extreme resample to 1/10 size is hardly reasonable, it becomes pointless.
Opinions vary, and this is a subject that we will keep coming back to. It is a popular claim that we should scan at only even divisors like 75, 100, 150 or 300 dpi, and then resample the image to be smaller to get the final size. This idea claims that elaborate image programs (like Photoshop) can do a better resampling job than the scanner can. More on this later, but I have to agree, sometimes it can.
Wrestling with the huge images probably builds our fortitude and character, but it's probably best to just scan to get the image size you need in the first place. And it's so practical.
However (there's always a however 😊 ), it is true that if the image might be resized after the scan, it's always much better quality to resize to reduce the image size rather than to resize to increase the image size. If you aren't sure what your future intentions for the image might be, and won't be able to scan it again, then it's probably best to err on the large side (if storage space allows, up to reasonable amounts anyway). Resizing to be smaller discards excess pixels. But resizing to be larger must create (or fake) new interpolated pixels which were not in the original scan. There is no additional detail possible in interpolated pixels, even if the image is larger. The results are not at all the same as scanning at the higher resolution.