A few scanning tips
Me too, but my preaching about 200 to 240 dpi being needed for today's good inkjet printers is scaled "at the paper". If printing at the original size (100% scale), then that is also the proper scanning resolution. But if enlarging the printed image, then it will certainly require more scan resolution for the best results, as just explained in the section on scaling. And this can be a problem.
The problem is this: If you want to print an image at 200 dpi at the paper, and you want to print it at 2 times the size of the original, then you need to scan the original photo print at 2 x 200 = 400 dpi in order to have enough pixels to scale it this large, to achieve 200 dpi at the paper again. The scanning resolution is the printing resolution multiplied by the enlargement factor (this is true regardless if printing at 200% or 50% size).
Let's say it one more time: The ratio of (scanning resolution / printing resolution) is the printed enlargement factor of the original. If you scan at 300 dpi and print at 150 dpi, it will print twice the size of the original. (300/150 = 2X)
If you will enlarge a 4x5 inch photo to print 8X10 inch size, and if your printer likes 200 dpi, then it's disappointing to scale the size back to 200/2 = 100 dpi on paper. Theoretically, you instead need to scan 4x5 inches at 200x2 = 400 dpi to allow scaling back to 400/2 = 200 dpi for 8x10 inches, as was discussed before. If you want to print 3X size at 200 dpi, you should scan at 600 dpi to have enough pixels to scale to 200 dpi at 3X size.
Note that this will produce a really huge image (pixels and bytes), and there are other practical issues too. Let's be realistic about printing enlarged images. In the real world, we really don't benefit much from scanning color photo prints at resolutions of more than 300 dpi. Many images are not all that sharp, and 200 dpi is often plenty. Scanning film can do very greatly better, but 300 dpi is pushing the limit of what color prints have to give.
Therefore, enlarging color prints to print 2X or 3X times original size is often a little disappointing, the results won't be as sharp as we might have hoped for. It certainly will never be as sharp as the smaller original. You can scan the photo prints at 600 dpi, and the pixels will indeed be smaller then, but when you scale and print these images, all the fantastic detail that you might have hoped for won't really be there. The result can be decent, but there won't be any miracles.
NOTE: B&W prints can be better, depending on factors like degree of original enlargement. Old historic prints were often contact printed from very large negatives, and 600 dpi might be useful in some cases (if you need that size). But color prints typically don't often offer much over 300 dpi, and sometimes 200 dpi. This represents a practical limit preventing perfect enlargement of scanned color prints.
Assuming your computer's memory will tolerate it, then if you do need to print 2X size at 200 dpi, do scan at 400 dpi. If you do need to print 3X size at 200 dpi, do scan at 600 dpi. If it is not a pain to do it, sure, why not? But don't be surprised when your enlarged results are not as detailed as you might have assumed. There are limits to what we can do well. 150% enlargement from prints can be pretty good. And 200% is not too bad, but 300% is asking a lot from enlarging color prints.
But if your computer's memory limitations will not allow such huge scans from color prints, you are really not missing much. I'd suggest scanning at 300 dpi, just for the warm fuzzy feeling of knowing you have done everything that is possible, and that you have obtained everything available in terms of original detail. There won't be much difference in the printed image than if you had scanned it at 600 dpi. Yes, you'd like to have more detail than this for the printer, but you don't often get more detail from a color print than what 300 dpi will give.
The good answer for creating huge images to print large is to use a film scanner to scan the film instead.