So do the Companions then the MQ and then the civil war?
That's what I've done. But I'm especially careful. Once, after having reached level 57 I discovered the Companions line was broken. And it all to do with the Hired Muscle quest you can get from them. It's one of the first quests you can get. It's not given every time and sometimes it's never given at all. Briefly, the quest is to intimidate an NPC but the Civil War destroys his house in Whiterun and thereafter he's nonexistent. This means that if you're given the quest, you can't complete it and therefore the Companions will never give you another quest because you haven't completed Hired Muscle.
Note that Hired Muscle may never be given to you. So while it's not for sure that the Civil War will break the line, you don't want to put a hundred + hours into it only to find yourself out of luck.
As for commpleting the MQ, I say that to make sure that you get the Cornered Rat quest. In short, there's a bug that can occur where you're never given the quest and therefore can't complete the MQ. At least get to that point in the game before going off to do anything else. That was another thing I discovered after being at Level 61. I'd done some of the MQ before deciding I wanted to do a lot of other stuff. So when I came back to it, it was broken. I don't know if it had anything to do with the Civil War, but it's better safe than sorry.