Various shops and merchants become available on the world map as you progress and complete requests. These include the Material Merchant, who sells common and sometimes rare materials, and the Weapon Merchant, who sells basic weapons. While the weapons sold aren't usually top-tier, they can be useful for fusion fodder or for quickly equipping new characters.
The 'Hylian Research Lab' and 'Royal Ancient Lab' services, once unlocked, offer unique upgrades and services related to the Sheikah Slate and ancient technology. Regularly check all available shops and services, as they often update their inventory or offer new features after certain story milestones or completed requests. Spending rupees wisely at these shops can significantly aid your progression.