When you set the DBMS Type to "MSSQL Express" then it requires using Windows Authentication to connect to the SQL Express instance. If the Audit Trail service account is running as an account with rights to SQL, then that should be fine. Just click the "Update" button and then you should be able to move onto the "Date Ranges" tab and configure a date range. Once that's done, a database should be created.
If you set the DBMS Type to "Standard MSSQL" then you can manually specify the SQL instance (even SQL Express) and also choose how you want to authenticate (Windows Authentication or Database Authentication). Then just click the "Update" button and then you can move onto the "Date Ranges" tab.
If you are getting any errors when trying to "Update" the database settings or notice that the database isn't getting created after you set a date range, then it'd be best to open a support case and provide the full text of any error messages you receive as well as the complete application event log.