The following tools will be made available once you talk to the characters for the first time and trigger their first memory. They cannot be purchased anywhere, but you can purchase upgrades to the axe, hammer, watering can, and hoe from Brutus the blacksmith.
If possible, you should try to obtain all the tools on day 1.
Tool
Description
How to Obtain
Axe
Used to chop down trees. Can be upgraded by Brutus.