FBX format is much preferred than OBJ because it can have embedded textures in it.
Have you tried checking the FBX model in 'FBX Viewer' official tool by Autodesk? If the textures are grey in there, then it might be a problem with exporting the model from your software. Please make sure you have 'Embedded media/texture' toggled on when exporting.
If that doesn't help - you can import the textures as PNGs to the assets folder and then reassign them to the model.
Let me know how it works out for you.