Opening Gloomhaven is an event. It is not something to be started unless you have at least an hour, a large clean space, organizational skills, and boxes - many additional boxes. I lost one piece when I opened and stored my copy of Gloomhaven, an enemy standee, and if I had been better prepared I may not have. (Side note: Cephalofair has a replacement policy.)
It is required that you have at least some containers when you open Gloomhaven, because nothing is provided for the hundreds of tokens you want to keep separated and not in the garbage. This guide is not how I packed Gloomhaven away for the first time. It is what I have come up with after many sessions to be a simple, practical, and functional sorting system for easy set-up and break down.
For all enemy tokens, terrain tokens, and a few other of the larger tokens, you can purchase two 17 Compartment Embroidery Floss Organizer, Clear $2.99 from Michael’s (for some reason a seemingly mirror version exists as well).
The Counter Tray will fit with the scenario materials and standee holders inside Office Bigso Marten Letter Box (more colors available) $12.99 from Container Store, or Amazon at higher cost, but with free shipping.
That is all I needed for storage in the home, costing about $30. If you are traveling with the Letter Box you should be careful that the lid does not come off. How you set it all up and what websites you use to manage the game are another story.