I'd recommend using the FBX Exporter... next be sure that 'Selected Objects' and 'Active Objects' are UNCHECKED., this will just output your entire scene "As-Is" to FBX.
There's no need to assign a material per se., but I would recommend creating a Base Material that you assign (even if you have no intention of using it)
Also., while I tend not to use Blender much for modelling., something I do out of habit today with Maya is with a new Scene, disable "Show Backfaces" because with Maya when this is on; this will show Front and Back Faces as if they're the same... but as most Renderers only support Single Sided Faces; this results in most being turned inside out (or unviewable) without writing a Double Face Shader.
Generally this means the Normal Faces need to be Flipped to become Forward Faces... this could potentially be an issue.
Another could be that you have automatic Show/Hide Objects with Selection; and the Export Function just does a "Raw" Dump of the Scene as an Exported Object; so if the Object is "Hidden" in Scene it's also "Hidden" in the Export.
Something else you could do though is to use a Rooted Object... so ensuring that all of the "Sub-Mesh" are part of a Main Object within the Scene.
In this regard typically speaking they'll all inherit properties from the Root Object.
