For central A/C, you'll need ducts and vents. Once you have the ducting in place anyway, you might as well use it for both your heating and cooling.
For a three floor house, you definitely want some kind of zoned system, with a thermostat on each floor. (I wish my 2-floor house was zoned.) You may want multiple cooling systems, or maybe one system with motorized dampers to control airflow to the various floors. Your HVAC contractor should be able to make a reccomendation of what will work best.
Whatever you do, do not skimp on the ductwork. Your HVAC contractor should run calculations on how big the ducts need to be. For many home builders, HVAC is a minor concern in the bulding plan. Make sure everything is sized correctly. Changing ductwork after the fact is very difficult. And if you don't have proper ducting, it won't matter how good your central heating using is.
For new construction, Geothermal is usually a good candidate. It can provide heating, cooling, and hot water with crazy efficiency. The installation cost is MUCH higher though. (There are tax credits that will offset some of the cost.) If you aren't up for geothermal, I would go for a traditional air-sourced heat pump for your heating and cooling needs. They are pretty efficient (at least in moderate climates). You are pretty much in the perfect lattitude for a heat pump.
However, I would not have the heat pump (air-sourced or geothermal) as your only heating system. Some kind of alternate (non-ducted) heat source would be a good idea. Heated floors, gas fireplace, etc. Air-sourced heat pumps lose their efficiency in very cold weather. And it can also be nice to have gentle air convection, vs a duct that is blowing in your face. You also have a backup system in case your central heat fails.
That said, ducted air is nice, because some regular circulation of air in all the rooms of the house avoids that "stagnant air" smell, as well as cutting down on dust, dander, etc.
Also, central air systems give you options for humidification and de-humification of the whole house. Look into that. It is usually a minor cost increase in the system, but can make a major difference in comfort.
Proper seasoning is going to take longer than that. Most experts recommend you buy green firewood in the spring, to let it season in the rack over the summer. A minimum of 6 months' drying time, leaving it exposed to the sun and protected from moisture, is needed to "cure' firewood.
DO NOT burn your green firewood. It will smoke, smoulder and not heat the chimney properly for good draft, so you'll get backdrafts into your home. I had this problem even with seasoned but dampened logs from my rack outside; the wood wouldn't burn properly even with a nice hot bed of coals under it, and we got a lot of smoke coming out the front of the fireplace (and up into the upper story of our house).
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Actually there are a few considerations you need to take into effect.
You first need to look up the "R" factor required from combustible materials for your specific stove. Every manufacturer has a safety insulation factor. This can be provided by materials such as concrete board, high density fiberboard insulation, steel sheets and air barriers. The factors can be different from the bottom, sides and back of a stove, so it is important to have the full specs. You should also check with the local building inspector to get the minimum distances from combustibles in your area. I believe most communities use the NFPA specs, but always check local requirements.
Practically speaking, using a single piece of concrete board under a wood stove is rarely enough insulation factor. I think 1/2" concrete board only has a R-rating of 2 or 3, which is much too low if attached directly to a wood floor without an air space. I would feel much more comfortable with a layer or two of brick or brick over high temp fiberboard insulation. High temp fiberboard can be rated as high as 800 degrees F per inch at 6 inches away from heat source. Available at any HVAC supplier.
After all the work you have done on your yurt, be absolutely safe and sure of you woodstove installation.
Good Luck my friend.