Unless you have a very small list of people, selecting by first name would seem very problematic. Couldn't you get two people with the same first name?
I'm assuming here that you have a FileMaker table where you have defined your field with the drop down. If so, you need this relationship:
FileMakerTable::PeopleID = SQLTable::IDField
Your drop down list would be set up as a 2 field value list with SQLTable::IDField in field 1 and A Name field from SQLTable in field 2. A field that combines first and last names would be a better option than first names I would think and I'm not sure how you would add that here since the data comes from the External SQL table. This assumes that there is an ID field (not a name) that uniquely identifies each person in the table.
With this setup, selecting a name, enters ths associated ID field and creates a link between the current record in your FileMaker table so that related data from the SQL table can be displayed or copied into your FileMaker table. Which is the best option for you depends on how you need to use this data and what should happen if the information for this record in the SQLTable should be edited in the future.
Here's a link that provides details on both methods: Auto Fill