I just wanted to post and share what I have been using for storage to and from tournaments and casual games. I've been using UltraPro Deck boxes (normally for MTG), which you can buy 5 for $10 on Amazon.


Along with those, you can fit a team of 20 dice perfectly in 3x4 bags that I got courtesy of Jo-Ann Fabrics,


You can fit two team per box, and two bags of 20 dice each. I will bring two teams in a single box, and two sets of sidekick dice in another box with every color basic action backer. It's really convenient because when you setup a game you just need two bags of dice, the only separating you will have to do is to set up your team. It's cheap and easy, with 5 boxes you can have a total of 9 teams with room for sidekick dice and action dice, all for about $15. Best thing is, you can just keep other bags handy, for a quick switch! The bags also are great for storage in general, you can fit more than 20 dice per bag, probably close to 24 dice if you squeezed in.