The collapse and its specific logic
The specific nature of your apocalypse determines everything about the world your survivors inhabit: what physical infrastructure survived, who has socially useful knowledge, how quickly civilization fell, and what kind of recovery is even theoretically possible. Writing the collapse with specific logic requires working backward from your story's world to the event that produced it, checking that the aftermath is consistent with the cause. A world destroyed by engineered plague has specific details that differ from a world destroyed by nuclear exchange, which differs from a world destroyed by ecological collapse. The specific cause of collapse also generates the specific fears and traumas that your characters carry: pandemic survivors carry different psychological weight than war survivors.