You should use a NADCA certified duct cleaner that cleans under negative pressure so they don’t do damage to the rest of the home. Be prepared to clean the house after, just to rid your entire environment of contaminants at one time. I personally would use one of the botanical products like EC3 or Benefect to clean the multitude of surfaces of a home.

From there I would focus on installing filters that are equipped to filter out as many particles as possible. Most Merv filters aren’t blocking out small enough particulates, so they pass right through and continue to circulate through a home. Mold spores can be as small as 2 microns, and hyphae fragments are even smaller so you need a product that can handle these microscopic particulates. I would purchase a system like the Intellipure whole-home air purifier that can remove particles as small as 7 nanometers to ensure the air in the entire home is as clean as possible.