Issue No 2: The nationality of the new coach. Chief executive David White says the door is open to worthy applicants from around the world but his preference is for a New Zealander. Former Australian wicketkeeper Steve Rixon and Englishman Andy Moles have done the job with vastly different results.
Rixon was popular, forthright and got good results out of a bunch of strong personalities in the late 1990s; Moles was a disaster, had no respect from the players and finished up a man alone in the dressing room.
There are several overseas coaches with decent track records who should at least warrant a serious conversation.
But if it's to be a New Zealander, former captains Stephen Fleming and Dan Vettori are in the conversation, along with current assistant coach Craig McMillan.
If lines of succession matter, McMillan is in the pole position, if he wants it. But there might be questions about whether he's got the very best out of New Zealand's batsmen in his time overseeing that side of the game.
Fleming's got proven success in T20 cricket; Vettori is also now a well-travelled short form coach.
Does it matter if any of their former teammates are still in the team? If so, then Fleming, who retired in 2008, would not be a candidate until Ross Taylor and Tim Southee have departed; Vettori, who stepped away after the 2015 World Cup, played with several more than that.
The maturity of the individuals counts in that situation, the ability to switch from having spent years sitting alongside someone, a few beers in the bar, or talking nonsense in down time to being the guy who looks a former teammate in the eye and says 'sorry mate, you're dropped'.
Issue No 3: Does it need to be a proven international coach?
New Zealand's major association coaches would therefore be out of the frame, although the likes of Gary Stead at Canterbury have spent time in the national squad set-up.
So there's plenty to cogitate in the coming months.
Where there should be no dispute, though, is the importance of Hesson to the national team.
Brendon McCullum, with the way he pulled New Zealand around in terms of playing philosophy and results, is perhaps the most important figure in New Zealand cricket in modern times, but Hesson's presence has been significant.
He wasn't without fault, but got his black spot - clumsily replacing Taylor as captain for McCullum - out of the way early. No one disputed McCullum wasn't the better leader, but NZC as a whole deserved, and got, condemnation for the way the change was handled.
Hesson could be a tough operator who wanted things done a certain way and got the best out of most of his players.
It helped having McCullum and the batting expertise and growing leadership skills of Kane Williamson to work with. Players such as Trent Boult, Taylor, Southee, BJ Watling and Neil Wagner haven't hurt either. But someone has to be puppetmaster.
Hesson's replacement(s) will inherit a quality landscape. There should be a demand of the new person akin to that asked of noted rowing coach Noel Donaldson when he took over the guiding of champion pair Eric Murray and Hamish Bond halfway through their stellar eight-year unbeaten run: do it the way you want, just don't stuff them up.
