My GH is wood and glass. I usually brush down with a stiff brush, then spray with armillatox (diluted as per instructions) and let dry off.
Looking at the question again, I just realised this is your first season, so you're not trying to get rid of nesting spider mites/ any other diseases that might have developed, just need the glass & wood to be clean in the conventional sense. I would use either window cleaning spray or washing up liquid with vinegar added.
Use disinfectant next time :)