There are three basic concepts, for distribution of heat, in home heating systems used today.
A forced air ducted system is the most common in much of the country.
Air conditioning and humidifiers are incorporated into these heating systems quite easily, and it is commonly done. Filters are added to the system for some degree of air cleaning. Filters are usually the only regular maintenance required besides a seasonal check.
Heating for this system may be provided in several ways, but a furnace fueled by gas or fuel oil is the most common. These are available today with efficiencies of over 90 %. The highly efficient furnaces require a drain to dispose of water condensed from flue gases, and they are often called condensing furnaces. They can be vented directly out a wall with PVC pipe. All combustion air can be drawn from outside, so there is no source of ignition that is not isolated from the air in the home. If you use a direct vent or forced vent water heater as well, it means no chimney would be required.
I believe that direct vent heating equipment is safer than other types. The lack of a chimney lowers costs on new construction. It frees up space, and there is no roof penetration as a source of possible leaks.
An air handler or fan coil unit can be used, as well. With this method, heat can be sourced in different ways. A boiler or other hot water heater can be used. Solar heating can be used by itself, or as a supplement to other methods. Heat pumps can provide the heat, which can be drawn from the air, the earth or groundwater. In rural areas an outdoor furnace may be used, which can burn coal, wood, or other biomass. (An outdoor furnace may produce unacceptable levels of air pollution in some areas). Other sources of heat may be available locally.
Care must be taken to balance these heating systems for even heat distribution. If you are using a furnac,e then proper sizing is important to ensure comfort, and to prevent short cycling. Too large a furnace will run for very short periods at a time causing inefficiencies and maintenance problems. You will need to do a heat load analysis to determine the size of furnace needed. If your home is small, super insulated, sealed, and utilizing passive solar gain, it could be difficult to find a furnace small enough.
Alternately, if your home is going to be large and complicated it could be difficult to balance a forced air system, resulting in uneven heating.
Be aware of the difference between input and output when sizing a furnace. A furnace of 100,000 BTUH input has an output of 60,000 at 60%, but produces 90,000 at 90%. Simple but easy to miss.
BTUH is British Thermal Units per Hour, and is still commonly used in the U.S.. The H may be dropped on rating plates. The metric equivalent of a BTU is 1055 joules. Although Canada officially uses the metric system, we often end up using a confusing mix of the two because of the influence of our large friend and neighbor, who also often uses a confusing mix of the two. I often use British units when writing because many of my readers will be American. I am familiar with both, as are many Canadians.
Radiant heating is the next most common heating system.
It uses water, or a mixture of glycol and water to distribute the heat, in most cases. Sometimes called hydronic heating as a reference to water. Electric heat is also distributed as radiant. Sometimes with a fan assist. Fireplaces are also a form of radiant heat, but are commonly fan assisted these days. As an aid to understanding radiant heat, you can think of the sun. It heats the earth and the objects on it with radiant heat. The warmth passes through the air without heating it. The air is heated in turn by contact with the earth.
This illustrates the purpose of a low E coating on windows. It slows the loss of radiant heat from the house in winter, and slows the gain of radiant heat from outside in summer. It has little effect on energy of shorter wave lengths, such as light.
Radiant heat can be very efficient. There are water heaters with efficiencies up to 97%. Check your codes, and with the manufacturers, for suitability before planning to use them. Extra efficiency is gained because the air is not heated directly, but rather objects (including yourself) are heated. You will be comfortable at lower temperature settings, and heat loss through ceilings and walls is reduced.
Hydronic radiant heat is distributed (who would have thought it) by radiators, or by incorporating radiant pipes or panels in walls, ceilings or floors. A common and very good method used today, is to place pex piping in concrete slabs, or directly under a framed wood floor. I have used both, and even very simple heating systems work very well. The warm floors are a real luxury.
Different rooms or portions of the home can be heated at different temperatures by using thermostats connected to zone valves. This also makes it possible to maintain an even heat if some areas of the home have different heating demands. It is even possible to use it to melt the snow on your driveway and walks if you use glycol in that portion of the system.
There as as many sources or combinations of sources that can be used to heat the water for a hydronic distribution system
You may be able to use one source to provide both domestic hot water and space heating. Plumbing codes, however, have been getting more restrictive for dual use in recent years. If your water is hard, it may also cause problems with mineral deposits. A water softener may be necessary to prevent undue maintenance issues.
One advantage of hydronic heating is the ease of adding solar as a supplemental source of heat. Another is that there may be less suspended particles in the air, since there is no fan blowing air around. This could be important if anyone in your family has respiratory problems.
Although it is not impossible to use a hydronic heating system for cooling, it is not possible to connect a conventional air conditioner to the system. An air conditioner does as the name implies. It conditions the air by cooling and removing humidity. (Once again, who would have thought it.) This uses different principles than a hydronic heating system.
A fairly recent innovation in heating and cooling is known as the Mini Split.
This system heats each room or area individually. Small units are placed in each area to provide heat or cooling, and are normally sourced from a heat pump.
That is about the limit of my knowledge about the system ,and I am not even sure how accurate that is. I will provide some links here, which I hope can explain it a little better.