Minimum brightness: the lower the better. Problem is, most manufacturers only specify the maximum brightness, which is useless for us as that is way to bright in most environments.
I have noticed however that displays with Quantum dot backlight or "RGB" spectrum displays like AMOLED seem to be way better for me than White LED technology in regards to brightness sensitivity (not taking into account other sensitivities). As I don't have to turn their brightness all the way down.
I think for people with brightness issues, Quantum dot displays (at least the ones who don't use White LED - sadly it seems some do) might be worth exploring. Provided of course, they don't have other design flaws like flicker, being connected to problematic input devices, or working on top of eye-straining operating systems.