I'm mostly a film-and-paper photographer: I take pictures, process the film and then make prints in the darkroom. The end-product of what I do is very definitely a bit of paper.
But I'd like to be able to show representations of these prints digitally (ie on the internet...). I'd be interested in knowing what the best way to do this is, and also how it's done professionally.
There are three obvious approaches:
The first of these is both hard and unappealing: it requires me to do a lot of work I'm not very interested in to reproduce what I already do in the darkroom, and also may or may not do a good job of representing what the print actually looks like.
The second I can do, and it should be reasonably easy. Keeping the prints flat is the hard bit, but I can mat them if need be.
I can't currently do the third, but I could buy a flatbed scanner if it's clearly the best approach.
I'd be interested in knowing two things.
Considering that you put a significant amount of work in at the darkroom printing stage then scanning the print is the best way to go. However this can be done either by yourself using a your own scanner or by sending the originals to a company that will scan them to professional standard. The second option I would only use if the images were to be reproduced in a published book. A lot of this depends on what the digitized images will be used for - reproduction in a published book, your website, social media sharing, archival purposes. If the digitized images are only ever going to be viewed on a monitor (ie. they won't be reprinted) then you only need low resolution scans of the original print. A decent flatbed scanner should easily do the job and it shouldn't cost that much.
Personally I would scan the originals myself except for those few images that will be published in print form in which case I would consider using the services of a company to do the scanning for me.
I recommend the second alternative, with some conditions.
I expect your prints to be often larger than A4, and a flatbed this size takes a lot of space, costs money, ...
If you have a wall available, place a vertical flat support on it, buy a piece of "museum glass" (it is basically invisible, no significant reflections, very thin, ...) and place the print between the two.
You can use a good dSLR to take the photo.
A square metre of museum glass costs about 350 Euro, which is about the same as a A3 flatbed scanner, which is smaller.
I'm not sure about flatbed, but the solution I propose allows you to take photos with zero visible reflections.
The way major museums and institutions such as the Smithsonian do it is with a large format camera using a digital scan back under very controlled lighting.
Such a setup combines the strengths of flatbed scanners while scanning at very high resolutions and cameras that give greater control over the lighting used.
More details about such a setup and how it is used can be found at this answer to:
If the end goal is a digital image file, then the last step (printing the digital image file at whatever size/quality desired) need not be done.
For your purposes, scanning the print makes sense, as @John Hawthorne explains. However, photographers looking to create a digital archive of their film photography should always work with the negative or slide. The original has far more information on it than the print can capture, and a good high resolution scanner will preserve more of the lost detail (though still not as much as in the original).
Excellent information on this is available from the Library of Congress, like Personal Digital Archiving: The Basics of Scanning.