If you want the emotional through-line for Bucky Barnes, I usually start with his origin scenes and then ride the wave of the reveal and recovery.
Begin with the Bucky moments in 'Captain America: The First Avenger' — the camaraderie with Steve and the fall that changes everything. Then watch 'Captain America: The Winter Soldier' straight through; it’s the core of the Winter Soldier identity, so experiencing the full film keeps the mystery and the blows intact. After that, go to 'Captain America: Civil War' to see the escalation and the personal costs of his manipulation.
Finish the arc with 'Avengers: Infinity War' (Wakanda battle) and 'Avengers: Endgame' (the final stand), then follow up with the full run of 'The Falcon and the Winter Soldier' to get the healing and the new life threads. Personally, watching in this sequence — origin, corrupted identity, fallout, battles, then rehabilitation — gives the best emotional payoffs and shows how the character grows over time.