It is difficult to give you a “one-size-fits-all” response to this question. Ultimately, an organization needs to assess their culture, strengths and weaknesses. Put together a move-forward plan that addresses the weaknesses, and leverages the organizational strengths.
What works for one organization doesn’t necessarily work for another. The biggest mistake I see occur, is when an organization launches their journey and they hire Black Belts to fix other people’s processes. This is not a good approach, and creates alot of resistance to process change. Always remember to ask: Are we doing process improvement with people, or to them? If it’s the latter, change your strategy.