Saving b&w photos in Photoshop.

Yes, I deliberately avoided the can of worms which is grayscale in my reply, just to keep it simple.

The overriding advice for grayscale is this: don't go there unless you know what you're doing. Much of the problem is that the Photoshop default working gray, Dot Gain (at whatever percentage) has a very idiosyncratic tone curve which bears little relevance to any modern workflow or output condition. The dot gain profiles are generic and by now very outdated profiles for offset print. Nowadays you use the K component in a CMYK profile for this purpose.

Another problem with grayscale is that many applications don't support grayscale color management (yes, I know; there's no color, but color management principles still apply. There's still a tone curve).

If you must work with grayscale, set your working gray to either Gray Gamma 2.2 or sGray. But sRGB or Adobe RGB are both much safer, even for monochrome.

Why are you involving grayscale at all? 

Are the images really going to be printed 1C? 

There are two things at play here:

• the tone response curve of the actual data. You need to standardize this, and the most practical way to do that is to convert to sRGB IEC61966-2.1, and to make sure that profile is embedded. Then it will be correctly treated in all applications that support color management. In those that don't, the sRGB tone curve is similar enough to most screens' native tone response curve that it should look basically right anywhere.
• screen brightness. This is more tricky. Setting a brightness level for the white point is an essential component in monitor calibration. In dealing with photographs and similar, we do in fact have a reference that we can all agree on: the brightness of white paper. Obviously, this isn't a numerical reference, but a strictly visual one. Lots of external factors influence perception, so what you want is simply to see the equivalent of paper white on screen. Try this visual test on your phone. It's probably way too bright.

If you use a calibrator on your computer, the white level according to these criteria will normally (under "average" indoor conditions) be in the vicinity of 120 cd/m². That's just to give you a ballpark figure.

The black point also has a huge impact on the visual experience. The deeper the black, the more punch. High-end calibrators will let you set the black point, but many don't, and you just have to live with the native black point. This will vary a lot with screen technology, but all of them will normally be much deeper black than you get with ink on paper or any other printing technology. Only a silver gelatine print of the highest grade can compete with an average computer screen.