I am also reading up on linked lists

This seems like it might be the way to go. A linked list, based on my understanding, is just a bunch of items that have pointers, aka links, to their neighbors. Perhaps one could use a table with columns THIS_ID, PREV_ID, NEXT_ID. Then only a few columns need to be changed in order to remove an item, add a new item, or move an item to a different location.

The problem with this approach, as I see it, is you then have to step through the whole thing sequentially in order to build your final ordered list. Perhaps there are some techniques to avoid this that I'm unaware of (I do not have a computer science background; I'm just a long-time amateur programmer).

If there are any other ideas, I'd love to hear them. It's always an education. 8^)

Update: to clarify a bit, I should have mentioned that I agree with some of the monks who say the order should be separate from the definition of the images. In other words, you might have one table called IMAGES with columns IMAGE_ID, IMAGE_NAME, IMAGE_SIZE, IMAGE_COMMENTS then a separate table named IMAGE_ORDER with the THIS_ID, PREV_ID, NEXT_ID columns.