public enum StartProjectMode : System.Enum, System.IComparable, System.IConvertible, System.IFormattable  

//Default options can be set regardless of the value of the "companion"
//path (to a project, folder, gdb, toolbox, etc.). The path value is ignored if
//the option setting does not use it. This is the same behavior as on the Pro UI.
ApplicationOptions.GeneralOptions.StartupOption = StartProjectMode.ShowStartPage;
ApplicationOptions.GeneralOptions.HomeFolderOption = OptionSetting.UseDefault;
ApplicationOptions.GeneralOptions.DefaultGeodatabaseOption = OptionSetting.UseDefault;
ApplicationOptions.GeneralOptions.DefaultToolboxOption = OptionSetting.UseDefault;//set default option first

//path values can (optionally) be set (back) to null if their 
//"companion" option setting is the default option.
if (ApplicationOptions.GeneralOptions.StartupOption != StartProjectMode.WithDefaultProject)
  ApplicationOptions.GeneralOptions.StartupProjectPath = null;
if (ApplicationOptions.GeneralOptions.HomeFolderOption == OptionSetting.UseDefault)
  ApplicationOptions.GeneralOptions.CustomHomeFolder = null;
if (ApplicationOptions.GeneralOptions.DefaultGeodatabaseOption == OptionSetting.UseDefault)
  ApplicationOptions.GeneralOptions.CustomDefaultGeodatabase = null;
if (ApplicationOptions.GeneralOptions.DefaultToolboxOption == OptionSetting.UseDefault)
  ApplicationOptions.GeneralOptions.CustomDefaultToolbox = null;