After you choose a nonland permanent, each other player does so in turn order starting from the player whose turn it is. Each player will know the choice made by previous players.

A permanent with indestructible can be chosen this way even though it wouldn’t be destroyed otherwise.

Once Fortunate Few begins resolving, no player may take any actions other than those specified by Fortunate Few until it’s done resolving. Notably, players must act to protect their permanents (such as by activating Kindred Boon) before knowing which permanents will be chosen.

Lands can’t be chosen and won’t be destroyed, even if they have other types (such as an artifact land).