There is no one method to doing anything. It depends on the artist and their preferences as well as the needs of the project.
Generally, if you have a lot of displacement though it's advisable that you make sure that renders properly. From there it can branch off in several ways. For instance, if it's a very stylized non photorealistic character then you'll obviously just have to paint a diffuse texture with built in lighting (and perhaps you will incorporate baked ambient occlusion). If it is meant to have lighting, but you're using an older shading model, then your spec/gloss maps will be following the old method (where you tighten up the gloss where spec is stronger and vice versa). And if you want reflections you'll have to create separate reflectance maps. On the other hand, if you're working with many modern shading models, specular/reflectance is merged into one attribute, which usually stays constant for one material, and highlights are instead controlled with roughness aka gloss, which automatically will dim/brighten highlights based on how rough you make the surface. Or it could be the metal/roughness workflow, in which case you don't need a specular map and you simply define which areas are metal or dielectric (this assigns a constant reflectance to dielectrics if the metallic is 0 and converts your color map to the specular if the metallic is 1). If none of what I said makes sense, you should do some reading on PBR, as you have no business painting maps if you don't understand what they're really doing.
I mainly work aiming for realism, and this is my personal workflow, generally: I make sure displacements work, adjust the scale as desired. I create/import a lookdev lighting setup (a neutral setup that lets you see the model clearly, this could be 3 point lighting, quality HDRI map). Now it depends what kind of model it is, but generally I won't start really doing lookdev yet.