So movement or perception? Aim or stroke mechanics?
I think that the mechanics of putting straight with good touch should come first!
Interesting segue into the full swing...Lots of full swing teachers are going to emphasise 'fundamentals' like grip, stance, allignment, and posture first, which undoubtedly are crucial. TGM seems to stress Basic and Acquired Motion with the above fundamentals blended in as necessary...as an order!