How does Promising Future resolve?
First, every player chooses and banishes a card, starting with the turn player.303.2.a Then, starting with the next player, every player starts playing their chosen card by putting it on the chain. The chosen cards do not proceed to finalization while Promising Future is still resolving.354.2354.3
Steps
Starting with the turn player and proceeding in turn order, each player looks at their top 5 cards, banishes one, then recycles the rest.303.2.a The cards already banished are public information, so each later player knows what the players before them chose.108.6.e
Starting with the next player and proceeding in turn order, each player puts their banished card on the chain as a pending item. Each card waits for finalization while Promising Future continues resolving.
Promising Future finishes resolving. This completes the act of playing Promising Future, so applicable abilities on cards such as Ravenbloom Student trigger and are put on the chain after the chosen cards.383.3420.4.a
The chosen cards then proceed to finalization in the order they were put on the chain: the next player's card first, followed by each other player in turn order.337.1.b Their base energy costs are set to zero, but their power costs, applicable additional costs, and later cost increases still apply.356.1.b.2356.1.b.3 If a player cannot pay every required cost, that card's play process is undone and it returns to banishment.358.2358.5
A unit or gear that finalizes resolves immediately and enters the board.337.2359.2.c359.2.d Its own play effect is put on the chain after it enters.383.4.a.2 Any other ability whose trigger condition was fulfilled by that entry is likewise put on the chain after the inciting event.383.2.c383.3 Because those abilities were added after the chosen cards, every chosen card finalizes or leaves the chain before those abilities finalize.337.1337.1.b
If any finalized spells or abilities remain, the controller of the newest one receives priority.337.4 Players may then play Reactions.338.1.a338.1.a.2 In that case, after all players pass priority without adding another item, finalized spells and abilities resolve from newest to oldest.339.1340.1
Example
In a two-player game, the turn player chooses and banishes first, so their opponent knows that choice before making their own. The opponent then puts their card on the chain first, followed by the turn player. If both cards are permanents and both finalize, the opponent's permanent enters first. If both are spells, the turn player's spell is newer and resolves first, after any items played or triggered above it.