I think the turn schedule sounds great but maybe you could come up with a way to draw them out of a hat or use a spinner/dice to decide? We have a bookshelf in our living room that stores most of our games, with smaller games/card games in two baskets. It keeps them accessible, but neat and out of the way when we're not playing. My kids are older though, so not sure if that would be too tempting for little ones?
We decide ours by whoever is first to run to the game closet and pick out the game! When we have game nights we usually play more than one so that way everyone is happy!
