A gas furnace is the cheapest to run and one of the most efficient furnaces out there today. You will find that when you are replacing your furnace the cost depends on what type of furnace you choose and the size. Of course a furnace for a 1,000 square foot house will cost less than a furnace that needs to heat a 3,000 square foot house.   Also, take into account the efficiency of the furnace you are choosing and if it is a multi-stage furnace.  A multi-speed furnace can produce heat at two or more different rates.   An even more efficient furnace is a variable speed furnace.  This system pairs a variable-speed blower with a computer-controlled thermostat. They both adjust automatically to maintain a constant temperature.  A variable speed furnace is by far the most efficient type of furnace and the quietest.