What you call a dropdown is a select field. In the simplest scenario if you want to have some predefined values you can use Common Data for it. Here is the post that explains it:
viewtopic.php?f=8&t=871&p=3070&hilit=commondata#p3070
and maybe this post will help you as well:
viewtopic.php?f=8&t=830&p=2904&hilit=commondata#p2904
Since you are customizing the recordset via Admin GUI with Record Browser admin utility, you need to first create new Common Data array, create some values there and then create new field with Commondata type and point to your custom Common Data array you just created.
Here is an example of the definition of Common Data field used in Tasks.
Field definitions:
Status field definition - based on Common Data: CRM/Status. Leave Value display function empty:
Here is the list of top level CommonData tables:
CRM/Status CommonData table - this is the name of the table we will read values from:
and values themselves:
