You do not have an air handler or ducts to distribute cooled air through your house. The installtion on a central air conditioning system will be fairly expensive and disruptive due to the need to distrubute cooled air. You will need the air conditioning condensor, evaporator and a blower system and ducts.
It is possible to install multiple smaller systems as suggested by Dan in the attic and basement of the house. That way, the air distrubution can be ducted through the basement or crawl-space floor to the first floor, and the attic system can duct through the second floor ceiling.
I think your next step is probably to contact a heating and air conditioning contractor. Do all the ususal check references and recommendations of friends. Get a couple estimates. The contractor will make recommendations. You have the advantage of being able to distribute this work over time (i.e. do upstairs system first).
Since the house has no air ducts currently, it is easy to understand why room (window mounted) air conditioners have been used up to now. There may be some additional ideas posted here, so keep in touch and good luck.