If you are aiming for high completion, follow this general order of progression:
You will need 13 red Heart Containers (temporary yellow hearts don't count) to pull the sword from its pedestal in the Lost Woods. the-legend-of-zelda-breath-of-the-wild-repack-incl-dlc-2022
Engage in the lengthy "From the Ground Up" side quest to build a new town from scratch, which eventually unlocks rare item vendors. If you are aiming for high completion, follow