A Full Installation is the most common type of HVAC installation for a reputable contractor. The ductwork adds two days of labor and about $2,000 to $3,000 to the price, but realize that this is a very important part of your HVAC system. Although it might sound like a good idea to reduce HVAC installation cost and get a quick change-out, realize that there is dirt and debris collecting in your ducts, and the ducts themselves develop holes and full breaks over the lifetime of your unit, all of which may be hidden from sight by insulation. Remember, many contractors will push a quick change-out on you because it is easy and good money for them – you need to be involved and ask questions.
Roof-mounted systems have the heating and cooling systems in one cabinet. Sometimes called "gas packs" (if the heater uses natural gas), they typically cost less than a comparable split system. In dry regions, most homes originally had "swamp-coolers" installed. When replacing them with HVAC systems, it's often cheaper to use existing mounts and ducting.
Free cooling systems can have very high efficiencies, and are sometimes combined with seasonal thermal energy storage so that the cold of winter can be used for summer air conditioning. Common storage mediums are deep aquifers or a natural underground rock mass accessed via a cluster of small-diameter, heat-exchanger-equipped boreholes. Some systems with small storages are hybrids, using free cooling early in the cooling season, and later employing a heat pump to chill the circulation coming from the storage. The heat pump is added-in because the storage acts as a heat sink when the system is in cooling (as opposed to charging) mode, causing the temperature to gradually increase during the cooling season.
In addition to the information below, see these two articles for the general care and maintenance of your air conditioner: Preparing Your Air Conditioner for Summer and How to Replace Furnace & AC Filters. Most noteworthy, you should replace the filters at least twice a year, before the heating and cooling seasons. For information on furnace problems, please see Furnace Not Working.