If you want to do the Civil War before the Main Quest, I strongly advise you to complete the civil war quest storyline before attempting the main quest. There are known issues with quests when you're sort of part of the way through both storylines, or trying to do both at the same time. There's a lot of overlap between the civil war and the main quest, and so people get strange glitches or are otherwise "stuck" with broken quests, quest objectives not progressing, etc.
That being said, I can't comment on how the game flows if you do Civil War and then Main Quest, since I've only ever done them in the reverse order, or had characters do one but not the other.