After the introductory "Aftermath" mission the game says to take two story mission cards.

1) Do we pick one or both of these to play/record in our Side Mission on the Campaign log?

2) Are we required to play both before the story mission?

3) Are we required to play the missions in order on the campaign log?

Play them in order on the log. You do the aftermath, then you pick one side quest from the two you are offered and play that one. Then you do the next story quest and so on.