For this approach you need to use a standard feature of salesforce called dependent picklists.
A dependent picklist is a custom or multi-select picklist for which
the valid values depend on the value of another field, called the
controlling field. Controlling fields can be any picklist (with at
least one and fewer than 300 values) or checkbox field on the same
To define dependent picklists: open your object settings page: click Create -> Objects, and select one of the custom objects in the list:
Scroll down to the "Custom Fields & Relationships" section and click the "Field Dependencies" button:
Then click on "New" and use the field dependency matrix to specify the dependent picklist values:
Then save your settings and you're done!