Who to avoid. It is usually a mistake to start with the most difficult people. Ideas new to the organization take time to become credible. Successes from groups one and two will have a better chance of convincing a skeptic than all the preaching and memos in the world. If you were to work with the most difficult group first, you would not only encounter resistance, you would increase the likelihood of failure stories spreading across the organization.
Bad news travels fast.
As for the laggards, ignore them. If you have a good solution, you should be able to find early adopters. By the time you deploy the solution to groups one, two and three, some of the laggards will have changed positions or left the company. If they are still in the organization, either the evidence so far will have converted them, or they will comply, albeit superficially, under the edict. You may need to leave the conversion of laggards to management.