I don’t know if you know this, but .obj format models typically have an associated .mtl file. The .mtl is what has all the material settings for the .obj model.
Generally for .obj models, it’s best practice to keep everything for that model together in its own folder. (.obj, .mtl, various texture images)
Sometimes materials wont work because of file path issues. (Relative vs. absolute) Usually it shouldn’t be a problem. But you can take a look at the .mtl with a text editor, if you’re curious.
Other than that, just plug and chug manually while getting a model setup for Blender. Sometimes with the things that can be added that aren’t supported in .obj it’s just better to enhance and re-save a model as it’s own dedicated .blend.