I clean and pack all my wigs away after the con. Some wigs become flat and can take on an odd shape when haphazardly thrown into bags or bins. So, before the convention or at the convention I steam them. Steaming relaxes the wigs and gives them body. Be careful doing this if your wig is styled or has hairspray as this can undo a lot of your hard work.
Steamers can be as cheap as 20$ and well worth the investment of not worrying about flat wigs.
I tend to leave wigs in the bags they came in.
I use a Build-a-bear box or a wig crate for my heavily styled wigs. (You can buy these on Amazon(USA PRICES DISPLAYED))
This also works for props
I label all my bags and store them in one bin to save room.
Here are some fun examples for storage as well.