The correct method to upgrade an unmanaged package that is installed in a production environment is to use the update link provided on the Installed Packages page. This process ensures that any modifications or additions in the package are properly integrated without the need to uninstall the previous version, thus preserving existing customizations and data.
A: Uninstalling removes all associated data and customizations, which is not advisable.
B: The Install Wizard is used for initial installations, not upgrades.
C: Installing to a Developer org first is a testing step, not an upgrade path for production.
Reference: Upgrading Unmanaged Packages on Salesforce Help