That is a very good question and I wish I fully understood what impact the staff has on the team, but I think the short answer is that you need the best staff that you can afford. There are so many variables that can determine your success or failure that all you can do is give your team every opportunity to be successful.
I play as GM only, so I look for a HC with very high ratings in at least two categories. Usually you can find a HC who is really good defensively or offensively and then maybe he is a good strategist or good at recognizing talent, etc...I then try to find assistants who can fill in the gaps. That's not really scientific, but it makes sense to me.
Also, no matter how good your coaching staff is, they are limited as to what they can and can't do. For example: In my Chicago Bulls dynasty, I had a backup point guard that was forced into a starting role in
game two of the conference finals. In the three games he started, he went 9 of 41 from the field, 0 of 35 from three and would not stop shooting. We lost two of those three games and it was at that point that I felt I needed to step in. I went into commissioner mode and changed the players playing style. I changed Pass to 100 and range to 100 in the Post to get him to stop shooting. It worked, but the coaching AI simply isn't sophisticated enough to deal with a unique problem like that.
Anyway, getting the best coaching staff you can afford can be tricky in my opinion. Mostly because the more you spend on coaches, the less money you have on training staff. I absolutely hate that. It seems like a crude way of managing the staff budget, which is fixed and non-negotiable. Ultimately you must find a balance between spending money for great coaches and sacrifice the training staff (Increased Injuries and longer rehab delay's) or have a great staff with mediocre coaches. I lean towards maximizing my training staff whenever possible, because no matter how good your coaching staff their staffs don't show up in the box score.