Pre-populate fields in Create screens with default values based on user's default team

We want to have fields in modules that are populated automatically based on the current user's team membership(s).  This needs to happen as the screen opens.  These fields may be of any type but I'm particularly interested in dropdowns.  These fields may also be read-only where needed.

The content of other dropdowns can then be populated based on the parent dropdown that has been pre-populated.