Hello:
If your not sure which mode to use, just choose one. I like
to use the integrated mode for the following reasons.
I use a dedicated SQL database with SMS which is why I use the Windows Security AKA integrated mode.
Windows Authentication, previously called integrated security, is the minimum administration overhead option for SQL Server.
This type of security maps the SMS Service account to the SQL Server database, and then it passes through the SMS Service account to SQL Server for validation and data access.
Sorry for the verbiage but it explains it in detail.