Geothermal Heat Pump
Efficiency
If upfront cost is of no concern, a Geothermal heat pump is the most efficient heating/cooling system. According to the Department of Energy, geothermal heat pumps can be between 300 - 600% efficient.
Financing
There may be government programs available to help fiance the installation of the system, as well as state programs.
Payback
Some sources estimate a payback period as short as 3 years, though actual results may vary. If you switch your main house over as well, use the system for hot water, and take advantage of government programs. The payback period could actually be quite short.
Electric Baseboard Heaters
Efficiency
Since electric heat is 100% efficient, every ounce of electricity used it converted to heat.
Financing
If there is adequate space and power available in the service panel, an electric baseboard heating system is fairly inexpensive to install.
Payback
Depending on the cost of electricity in your area, electric heat may or may not save you money over other heating options.
Natural Gas Room Heater
Efficiency
Since it's a smaller area, a standalone natural gas forced air system may not make sense. However, a smaller natural gas room heater (or a few) might make sense. Natural gas room heaters can be between 65 - 100% efficient (depending on the heater), so they can be quite efficient.
Financing
As with electric room heaters, natural gas room heaters will be fairly cheap to install.
Payback
Again, depending on the cost of fuel. A natural gas room heater may or may not save you money over other heating options.
More Info:
The U.S. Energy Information Administration has a Heating Fuel Comparison Calculator (Xls) that might be useful.
Best Answer
Very late in answering here, but solar pool heating systems are great and pay themselves off in 1-1.5 years vs. propane and electric heaters. They are -- by a large margin -- the most cost-efficient renewable energy application that I know of.
I see that you said solar pool heating requires a pool cover. It does not. A pool cover helps greatly, especially in a cold or dry climate: almost all of the heat a pool loses is from evaporation. However, it isn't really needed for solar. Is an uncovered solar-heated pool going to be 95 degrees Fahrenheit pool in the Winter? No, but it is going to give you 8-20 (depending on the size of the array) degrees Fahrenheit for free, which would costs thousands each year if done with propane.
Also, solar pool heating and propane are not mutually exclusive. You can easily get a system that uses both, heating the pool at all times with solar (provided that the panels are hot enough -- properly installed solar pool-heating systems bypass the solar if the panels are cold,) but if that isn't adequate, you can turn the propane on. As stated earlier, this setup saves thousands a year vs. propane. The solar portion of the system will pay itself off in ~1 year vs. propane, and it will save you $10,000-$60,000 over the life of the panels.