The "glare" looks like silvering to me. A common problem with old black and whites that are slowly coming apart. So what to do?
Either film or digital is OK (asuming that the digital camera has enough file size to use) but digital is easier because you do not have to scan the negative to get the image into the computer.
Lighting should be at a 45 degree angle from either side and should be balanced so its even.
Use double polorized light (thats with a polorizing filter over the lens and also over each light source. Turn the lens filter so that the glare disappears)
I find that this technique works very well not only for silvered prints, but also for paintings. However on paintings sometimes the artist would like a little reflection, so by adjusting the lens filter you can leave a little in the image.
Try it, you will like it!
Mike