Storing wine glasses upside down has some benefits, it protects the glassware from collecting dust in the bowl of the glass; but it also has a much larger negative, the ease of which that glassware can chip and break. If you plan to store your glassware upside down, you need to invest in racks — or hardware you can install in existing cabinets — that allows you to hang the wine glasses from their bases. Hanging the glasses keeps them off the floor of the cabinet, thereby protecting them from chipping.
If you don’t want to invest in the hardware that allows you to hang the glassware, make sure you store the glasses in a closed cabinet if possible, instead of out on an open shelf where they’re subjected to the elements. If you still find a bit of dust in the bowl of the glass when you go to pour yourself some wine, simply give the glass a quick rinse first. Just make sure you also dry the glass thoroughly after, so that you’re not causing the water to dilute the wine, or allowing the water to change the flavors of the wine with the chlorine and other minerals that were in the water.