The choice of creatures is made on resolution and not on announcement.

You can use mana abilities during the resolution of this spell if the player decides to pay the mana cost.

You choose whether to pay or not on resolution. If not, then you sacrifice the creature. You can choose to not pay if you control no creatures on resolution.

First the active player identifies the creature they control with the highest mana cost (and chooses one if there's a tie) and chooses whether to sacrifice it or pay mana. Then each other player in turn order does the same. All creatures sacrificed this way are sacrificed at the same time.

Although Tariff checks the mana value of the creatures on the battlefield, you need to pay the creature's actual mana cost (including color) to keep it on the battlefield.