There are many different types of central heating and air conditioning systems. The right one for you will depend on where your property is situated i.e. what type of weather conditions you get, the size of your home and your own personal requirements i.e. the size of your family. The idea behind any system is the same i.e. you want to heat the house when it is cold and cool it when it is warm. This will involve either moving air or moving water. All systems work on either one or a combination of these principles.
A gas forced air system is probably the most common central heating system in the US today. Basically a furnace heats the air which is then blown through your home by a system of fans. When you want to cool the air i.e. in summer, the same system takes the air in your home and passes it via a refrigeration device. That is the most basic explanation but there really isn’t an awful lot more to these systems. Do they work? Yes but they are not very efficient, are prone to being drafty and can result in needlessly high bills. You could have a standalone electric system which is popular as it is cheap to install. But it is expensive to run and you cannot add air conditioning to the same system so that is an additional cost should you need cool air in the summer.
You could have a water based system often referred to as Hydronic. A hot water system works on the basis that water is heated and distributed through your home via a system of radiators which then emit heat to those individual rooms. Radiators have become smaller and more effective than those in use in the 1960’s but it is still not an incredibly efficient system and cannot be used for air conditioning.
The best system is probably a combination of a couple of the above technologies. You should discuss your options with a professional Heating and Air conditioning systems company. They will be happy to advise you on the best option for your particular needs.