If you're asking you must not have natural gas available. If you are in a mild climate consider a heat pump. If not, try an oil fired furnace or a thermostat controlled pellet stove. Passive solar is great when the sun is shining.
Most AC repairs on this level are not "novice friendly" as there is a lot of electrical work involved. Consult a licensed electrician or consult your user manual before self-repairing.
Electric heating, natural gas, and oil are all alternatives. Oil and electric can be expensive unless you live in the northern USA but natural gas is usually affordable.
