A little simple math can help determine the size system you need. A rule of thumb is 20 BTUs per square foot. So, a 500 square foot room would need 10,000 BTUs to cool or warm it efficiently. This assumes that you live in a temperate region and have adequate insulation with no energy loss. In the real world, all units have some degree of energy loss. This is reflected in an HVAC system's SEER rating for cooling and AFUE rating for heating.
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Compressor -- Compressors are outdoor components in your system. The compressor is the pump that circulates the refrigerants through the air-conditioner. You can hear it when it's running so you'll know if it's working just by listening. If it starts getting louder, your compressor is about to fail. If it makes no sound when it should be on, it has already failed. Compressors fail for a number of reasons. Most often they fail due to strain from another failed part such as the fan motor. Electrical storms can also damage compressors. If the sound from the compressor gets louder or if you see a decrease in performance, you should have your compressor checked. A failed compressor will not heat or cool your house.
You've probably noticed many appliances boasting an Energy Star Certification. What this means is that manufacturer voluntarily built the product to help reduce greenhouse gases and meet non-regulatory guidelines offered by the Environmental Protection Agency. To earn an Energy Star rating, a product or system must be tested by a third party that has been recognized by the EPA for meeting their testing qualifications.
Cost Factors: The size of the unit, its efficiency and it’s single-stage, two-stage or variable-capacity are the top cost factors. Features like communicating technology and improved dehumidification performance also affect the price. Learn more about communicating technology here including the pros and cons, before being agreeing to a communicating system.

At the state level the rebates are still substantial. For example, switching to a zoned system can get you a $100 rebate from various A/C companies, and state rebates are also included. In Pennsylvania a high-efficiency air conditioner alone can get you up to $300, and a high-efficiency complete HVAC system can see up to $1000. Maryland's incentives get up to $1,250, with a $100 rebate on a tune up of an existing system.
With the split system, the evaporator coil is connected to a remote condenser unit using refrigerant piping between an indoor and outdoor unit instead of ducting air directly from the outdoor unit. Indoor units with directional vents mount onto walls, suspended from ceilings, or fit into the ceiling. Other indoor units mount inside the ceiling cavity, so that short lengths of duct handle air from the indoor unit to vents or diffusers around the rooms.

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.