After obtaining a grouping and sorting through everything, I scan the photos so I have backups in the event of a mishap. I usually do not mark on the backs of the original photos but I will mark on the scanned picture. I try to preserve the originals as much as possible so as not to introduce anything to the film or paper that could have long term affects.. Yes I know there are photo pens out there for marking pictures but this is just my thoughts.
Now putting my museum curator hat on, unfortunately there are many polices (which I do not agree with) that instruct us to mark on the backs of photos a catalog number. We have over 2500 rare photos in our museum collection and over the years these have been marked on the backs with pencil, pen, and other methods. There has been no accountability and it just makes me sick to see how an untrained person has ruined a photo with permanent ink or even worse they press down so hard to write on the back that the impression of the number now shows on the front of the photo.
It is the same with paper products that we have.. They are marked but to risk erasing the pencil marks is not worth tearing the paper or worse... Until the policies and procedures are changed, I am sorry to say that many more images and paper products may be permanently damaged by unnecessary markings. At the museum I work a now we are seeing the "sins of our fathers" so to speak and we are trying to correct old habits with new conservation/preservation procedures...
Now I can't condemn the museum professionals who were here before me, (At least the school trained folks) for they did not have the current technology we have today. Their scanners were copy machines and they placed the photo on the glass and made a copy of it. We do the same today with high resolution digital scanners but the quality is much better and in some cases safer to take digital scans... Others who were brought into the museum system who did not have the experience or knowledge were taught the wrong procedures and just told to "mark the backs with whatever" and hence the permanent damage has now been done..
So long story short, I scan the photo and mark on the scan and then preserve the photo by storing it in archival Mylar and acid free folders (marked on the front with what collection it came from)...
One of the books that I refer back to from time to time when I have questions/doubts about photos and their conservation/preservation/restoration... is from the Society of American Archivists called "Photographs, Archival Care and Management" by Mary Lynn Ritzenthaler and Diane Vogt-O'Connor.
Hope this helps