Here’s how I’m sleeving and storing the various types of cards in Arkham Horror: The Card Game.
Deck box: Ultimate Guard’s Twin Flip’n’Tray Deck Case 200+
I have the older version of this box, with only one removable deck section and the other fixed. I can fit all my tokens, plus my Chaos bag, in the removable tray. My character decks go in one deck box, the relevant scenario cards in the other.
Sleeves: For encounter decks and character decks, any “standard” trading card sleeves will fit; 63.5mm x 88mm as used for Pokemon, Magic the Gathering, and the grey Fantasy Flight sleeves. I’m using sleeves from one of my many Pokemon trainer boxes because they shuffle nicely and I have loads…
For Agenda and Act decks, as well as character ID cards and other double-sided cards, you need to use fully transparent sleeves so you can view both sides. My preference is for the Fantasy Flight grey sleeves, however they’re a bit pricey – sleeving a whole core or major expansion can cost the same as the game itself. Instead, I’ve found “Make Them Last” sleeves on Ebay. I use thick sleeves for cards that get a bit more use, and the cheaper thin sleeves for cards which are no longer used, or only used briefly. At the time of writing, they’re £1.40 for 50 thick sleeves (either size) or 100 thin sleeves.