When coaching beats boosting (and when it doesn't)
Boosting raises your rank temporarily.
Coaching raises your skill permanently.
If you only want to climb once and never come back, a boost is the shorter route. If you plan to keep playing, coaching helps you hold the rank you reach on your own, so you need fewer boosts later. One approach for serious players: a few coaching sessions first, then climbing on your own with a stronger skill base.