Be careful of dishonest HVAC contractors. There’s no magical formula to see if an HVAC contractor is scamming you, unfortunately, but remember that they typically do this in one of two ways: first, they are charging grossly low prices (far below everyone else), or second, they aren’t including what everyone else is. In the first situation, they will charge you change fees, other hidden fees, or they stole the equipment and are passing themselves off as legitimate contractors (very common in California these days). In the second situation, they are charging you a very fair price, but aren’t including what the other contractors are (i.e. charging $10,500 for the installation which is fair, but not including the ductwork which is a scam unless there is some other, complex stuff going on there).
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.
An EER certifies the cooling efficiency of HVAC units. It's calculated by the rate of the cooling in British thermal units (Btus) per hour and divided by the rate of energy input in watts at a specific temperature. The calculation goes as BtuH/WATT at dry bulb (db) versus wet bulb (wb) temperatures. The optimal rating for a cooling unit is about 80db/67wb inside and 95db/75wb outside.
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.
Before opening the electrical cover on the A/C unit, be sure to shut off all power to the compressor unit and the indoor furnace or air handler, and verify that it is off. Note that this may mean shutting off a circuit breaker that serves the furnace and air handler, and then, near the compressor, pulling out the disconnect block (or shutting off the 220-volt power) to the outdoor compressor.