One of the things I found difficult is reducing 'vertical stripes' in old photos. I assume they're scanner reflections of the paper grain. Sometimes the stripes are much worse in one of the channels (usually blue) so for B&W photos, find the channels with the least noise is a good idea. For colour photos, we need all channels. My usually good (Topaz) noise removal plugin has little or no effect on stripes. Fast Fourier Analysis (FFT) plugins are often recommended for reducing patterns but I've not had much luck with FFT on stripes (yet).
There are other plugins (like 'NeatImage' $40 - $50) which may be useful. But I found that one of the free Nik noise removal filters (Dfine2) did a pretty good job on stripes. You can play with the number of pixels in the filter to get the best balance between 'noise removal' and 'keeping the details'.
The Dfine2 filter reduced stripes (and other noise) but other details too. So after applying the filter, you need to restore the fine details. I use a history brush to 'paint in' the fine (unfiltered) details like facial features, sharp edges, texture of hair, flowers, dresses, collars etc.
Mike
