Becky, that is a problem I've been dealing with. Carpets don't help with the dust problem and dust mites that live in them so constant vacuuming is a must. Commercial office buildings use air filtration systems that exchange the air at least 8 times or more per hour and then run it through electronic air filters or hepa filters. I know a pharmaceutical manufacturing plant with aseptic areas that have hepa filters doing 20 air exchanges per hour to keep the air clean. That is a big air handling system.
I have been looking at a whole house hepa filter added to the furnace/ac or possibly a honeywell electronic air cleaner which will get most of it. Problem with a home is that the furnace only runs part time and will only clean the air that flows between the ducts and the returns which leaves a lot of dead spaces for settling. Turning the fan on all the time will help filter more dust but may be drafty when the furnace isn't heating in the winter. It does better in the summer. Ceiling fans will help keep the air moving.
Also think about a heat/energy recovery ventilator that brings in fresh air into the house while filtering it and expells bad inside air. Also think about humidity problems and humidification as well as dehumidification. I suppose dust is better than mold, mildew, and rotting lumber. There is no cheap fix. Think total environmental climate control. Just my thoughts.