Ideally, our coaching staff would be comprised of
1) the head coach
2) a primary assistant coach or associate coach who is second in command to the head coach, if the head coach is a good cop type of guy, this coach would ideally be a bad cop type, give things a little balance. If the head coach primarily focuses on forwards, this coach would focus primarily on D. The idea is to balance it out a little bit, somebody that will push the head coach to be better. They should have a healthy respect for one another, likely have worked together in the past at some point and are comfortable in knowing how to push each other without crossing each other.
3a) The second assistant coach would have a long track record of success on the penalty kill, like Dave Barr in New Jersey. At every level he's coached going back to OHL, Dave Barr has basically had a penalty kill at the class of the league. Seek out a guy like this. If year in year out he has devised a system that has adapted with changing times and still has the ability to be at the class of his respective league, I think you are pretty safe in selecting a guy like that.
3b) The third assistant coach would have a long track record of success on the powerplay, like Todd McLellan had in every team/league he ever coached in before he was brought on to Mike Babcock's staff. You're looking for someone similar to 3b but just with a different area of expertise.
Ideally, the philosophy of the team and management of individual player is disseminated from the head coach. The head coach sets the culture and how every team member and staff member is dealt with, I think a guy who appears to be great as a "people manager" first and foremost is Paul MacLean, that would be my primary consideration in choosing a head coach - is he a great leader of men. Each "department" would be ceded over to the defensive coordinator/penalty kill coordinator/powerplay coordinator. Obviously, the personalities have to fit, but this is what I believe would be the most ideal set-up. At the end of the day, a team is full of people not just players. This also allows the lower coaches to approach their systems with a more focused and obsessive approach.
Another thing I would LOVE to do is bring over a rising star from Sweden like Roger Ronnberg over (or someone of that ilk, maybe not him in particular, I'd probably have to do a little more research) and have him bring his views and approach to the game to North America and implement some more international philosophies. It can never hurt to bring in new voices and try to innovate.