The developer should use an external ID field to ensure the data being integrated is matched to the right records in Salesforce. An external ID field is a custom field that has the External ID attribute, meaning that it contains unique record identifiers from a system outside of Salesforce. When you integrate with an external system, you can use an external ID field to match records based on the external system's ID, rather than the Salesforce ID. This way, you can avoid creating duplicate records or updating the wrong records. An external ID field can also be used as a relationship field to relate records to other objects. A lookup field is a relationship field that allows users to select a record from another object. A formula field is a read-only field that derives its value from a formula expression. An external object is a custom object that maps to data stored outside Salesforce, such as in an external database. These options are not relevant to matching records based on an external system's ID. References:
* Salesforce Help: External ID Fields, page 1
* Trailhead: Platform Developer I Certification Study Guide: Data Modeling, unit 2