You can set up a default database for your users to search under Authentication/Access > Database Access inside the the FirstSearch Admin tool. Select the radio button of the database you want under the Default Database column to set it as the default and then click Save Changes.
If you prefer not to choose a default database, select No Default Database at the bottom of the list.
You can also force users to search a specific database by appending
&dbname=<database code> to the end of your URL link to FirstSearch. Here is a list of database codes.