Way to put me in a tough spot ;)
My philosophy is to work on golf the way I would teach any other sport. I'd start with set up/grip etc, and then I'd work on the goal of the swing. So I usually teach in this rough order: set up, impact, follow-through, backswing.
But there has to have some flexibility in the system. Last week I had a complete beginner who had almost a foot of sway off the ball in his backswing. We had to work on that first. But as soon as that was "good enough", we moved on to getting into a good follow-through position.
One of my other philosophies is that you can't perfect one part of the swing if there are big deficiencies in another. They all work together. So that's part of the iterative idea of why it's best to learn the swing in layers. The art of teaching this game is knowing when to move on from one area and focus on another.
If it were me, I would probably focus on these two positions.