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.
You don't have to worry about a heat pump being inadequate for cooling tasks, they are available in a large range of sizes. For really large buildings, they can be ganged together. 800 sf is a walk in the park for residential sized units.
I don't know the specifics of what determines when the backup furnace kicks in. IIRC, it is the combination of a lower thermostat set point and the outside temperature. It kicks on when the pump is not keeping up or it's too cold for it to run efficiently. I can assure you you will not be sitting for hours waiting for backup heat. No customer would sit still for such a system.
While it is true that heat pump heat is free, you are just paying to move it around, if you've had heat wave cooling bills before, you know moving heat around is far from cheap. Only a careful analysis of the various options, considering both operational and installation costs, as well as life cycle replacement, can you make a proper decision about which system is most cost effective. The correct solution will vary by small changes in energy costs and climate.
In cold climates, a ground heat source system should at least be considered because it will reduce or eliminate the need for backup heat. If you are concerned about your carbon footprint, do not forget most electricity generated in the US is by burning fossil fuels. Your footprint from using a heat pump will vary greatly depending on where your local power is coming from. Heat pumps make a lot of sense for many people, especially if they are investing in cooling equipment anyway. But everyone's situation is unique, so the best solution can be arrived at only after careful rational analysis of all the factors.
Best Answer
You're right, but only because oil is the worst, most expensive way to heat a home. Pretty much anything beats it, except maybe electric resistance in places with high electricity prices. Wood, gas, and heat pump electric will all beat the pants off oil. That said, even 80% efficiency may be optimistic for a modern high efficiency wood stove. But even if that's overstated, as you can see, it's still a pretty good deal.
Additionally, your calculations may even be understating the advantages of a heat pump. 1.4 as the coefficient of performance is very conservative. I'd use 2, especially given how they not have high-efficiency units on the market than can deliver their rated performance at -15f. Some can go as high as 3 or 4 during periods of non-frigid outdoor temperatures and less than peak internal load.
Edit: you said, "Does that calculation make sense? Are heat pumps and wood inserts really that much better than oil? Can I really save 178 dollars a month by going with a 16 SEER heat pump?"
Yes indeed. But again, only because oil is such an awful fuel. Anywhere in the USA, one therm of oil heat is several times four times as expensive as one therm of natural gas heat, simply because of the relatives prices of oil vs natural gas. If you were comparing a wood stove and an electric heap pump to natural gas, it would get a whole lot more complicated--especially in the cases of a 95% efficient gas furnace, or a state with low gas prices or high electric prices.
No matter what you choose, do your wallet and the planet a favor and heat with something other than oil! It's expensive, it's dirty, and (IMHO) it contributes to awful foreign policy. Just Say No!
Edit 2: Some gov't verification of your numbers: http://www.eia.doe.gov/neic/experts/heatcalc.xls