It may surprise you to learn that the HVAC (heating, ventilation, and air conditioning) system for a Quonset hut home isn't necessarily any different from a conventional home with a similar size and layout, for the most part. The determination of what type of system will work best for you will have much more to do with the overall size of your home, its layout, your local climate, your budget, and other possible local considerations such as the applicable energy code, if you have one where you will be building.
For some homes, a traditionally ducted, central furnace/AC system will be a good choice. For smaller homes, such as an open-concept studio or open plan one-two bedroom home, a ductless mini-split system could be a good option.
For heating, a geothermal or ground source heat pump will cost more to set up than a conventional heat pump would, but you basically never have to buy fuel (although the system will require some electricity to run).
Many Quonset hut homes feature a lofty, open great room that takes full advantage of the large, clear spans these buildings are capable of. These types of spaces can be a challenge to heat, but a great solution there is to embed tubing in the concrete slab for a radiant floor system. We have installed this in the Loft House at the Quompound and we absolutely love it. Rather than blow hot air around in the big space, which would be constantly rising up out of human contact, the floor is just gently, silently heated to a comfortable level using the same on-demand propane water heater that creates our domestic hot water. I wrote about that system in detail, here.
Lastly, a wood stove or pellet stove can be a good option for heating. I wrote up a separate FAQ on those, so be sure to check it out also.