We did it anti-clockwise going to Mangahuehu hut for the first night and then carrying on from there.Its probably not an issue which direction you go,just give yourself a spare day otherwise you could end up with the odd long day to catch up.My favourite hut was Rangipo but the whole trip is excellent.Hope the weather(and the mountain!) behaves.
The road walk can be easily avoided by going up the Blyth Hut and then navigating across country, above bush line until you intersect with the road further up. There is no track but it is easy enough going. It is also possible to find a route through clearings from where the the Mangaehuehu track joins the road to intersect with the Horopito track and then to Mangaturuturu. The only problem with this is that you miss out on the Mangaturturu cascades, which are worth a visit.
They're the standard iron stove so if you have them going hot there will be enough heat on the top to cook. I do remember leaving things on there but it took about 30min+ to boil anything because we didn't want to heat the hut up that much.