How to copy? . . . I am wondering whether I would do better with a scanner.
I have done it both ways and find that with the limited contrast range of a print, I get better results, in far less time, using a digital camera and processing raw images.
I use the basic polarized lighting (2 polarized lights equidistant from the subject elevated at 45˚ to the plane of focus) and a 90mm TS-E with circular polarizer. The photos/artwork is placed on black velvet and once everything is aligned the process is a quick production.
As for lenses, a "flat field" lens is best and with DSLR gear those are typically given the "macro" designation. Back in the day, I had a Canon FD 50mm macro with extension tube, and for large pieces of art it worked very well. It was extremely sharp at f8 - f11 and had virtually no pincushion/barrel distortion. For the small photos you're copying, the camera-to-subject distance will be very short so you might consider a focal length of 90-110mm to give you a better working situation.