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I would say focus your attentions on the does. They need to feel comfy with you more than the bucks do.
We keep ours in hanging wire cages in a well ventilated shed. Poops fall to the floor and I can sweep them up for the garden and the rabbits are never in their own excrement. The shed has electricity and I have a fan set up to help keep them cool in the summer. Shelves are nice because the rabbits like hopping from one level to another and it gives them something to do. We also give them trimmings from our apple trees to chew on, but you can use wood from the hardware store so long as it isn't treated. If they don't have something to chew on, sometimes they will overeat. Cedar isn't good for them, though, so don't give them Cedar.
The does, ideally, should have a larger space than the buck so there is plenty of room for her and the kits as they get old enough to leave the nest box. Breeding should occur in the buck's space. When you ask about having them together, do you mean in the same space or in the same hutch with separate spaces? Bucks will sometimes eat the kits, so it is not a good idea to have him in the same space with the doe. Also, keeping them together makes it difficult to record and control production. Having them in a single hutch with separate sections probably won't be a problem, though. With the amount of space the does need, though, your hutch would need to be really big to house all three rabbits plus the litters. 36x30 is the minimum recommended space for each doe. Bucks don't need so much space, but keep in mind rabbits like New Zealands get very big compared to most pet breed rabbits.
If you do not slaughter all of your buns at the same time, American standards recommend separating males and females by 3 months of age. I'm told the standard in Europe is to keep them together until six months old, but you will risk pregnant sisters by that age.
If you watch the does pretty closely, you can tell when they are ready to breed. They get antsy and start rubbing their chins on their cage.
I think if I were you, I would use that hutch for the buck. You said it is a three section hutch; are you able to remove the separator between two of the sections to make it larger? You could use that one for one of the does or as a place to put the kits as they get bigger if you want to give mom some space (though they can stay with mom right up until slaughter, particularly if you dispatch them all around the same time).
