A symbol is always assigned to the none class. You can edit the symbol itself and break down its parts. You can then apply different textures to different parts of the symbol. For example, you could apply a glass shader for glass, within a window symbol. We provide some generic classes (style 1-15) in templates just for this purpose.
Custom Objects are easily textured as there are fields available in the creation dialog for texture information. If this object is then saved as a symbol, the texturing information is retained.