This information will help clarify and answer some of the questions.
New or existing system: Knowing your plans for A/C installation will help your service provider give you a more accurate estimate. For example, if you are tying into an existing system, odds are you will want to use the same brand as the older system. Completely replacing your system will call for tearing it out and having it disposed of both jobs that could mean additional cost to you.
Addition or remodel: Knowing whether an addition or remodel is in process will help your service professional size up your air conditioning needs and give you a more accurate estimate. A house's structure, window area, sun exposure, and the climate will affect your cooling needs.
Power: A central air conditioner's cooling capacity is rated in Btu's (British thermal units) per hour. As a rough rule you need 12,000 Btu's for 1,000 square feet of well insulated space or 400 square feet of poorly insulated space. If you have high ceilings, your cooling needs will be different; it takes more cooling power to maintain a comfortable temperature in the house.
Aging system: Air conditioners have become increasingly energy efficient in the last decade. If your system may have cooled better days and nights years ago, you may want to consider having it completely replaced. If your service professional is tying into an existing system, the older system's age will help determine its compatibility with the newer system.
Wall access: Knowing how much open access is available will help your service professional give you a more accurate estimate. Installing central air conditioning requires access to the home's heating and cooling duct system. The more open access there is, the less labor that will be involved.