The Cadillac of home insulation is spray foam insulation (SPF) which has no dust particulates and also creates a vapor barrier when installed monolithically. The cost usually limits who installs this type of insulation because the application should be done by trained and approved installers depending on your state restrictions. According to the EPA (https://www.epa.gov/saferchoice/spray-polyurethane-foam-spf-insulation-and-how-use-it-more-safely) SPF is a highly-effective and widely-used insulation and air sealant. However, exposures to SPF’s key ingredient, isocyanates and other SPF chemicals in vapors, aerosols, and dust created during and after installation, can cause: Asthma, Sensitization, Lung damage, Other respiratory and breathing problems, Skin and eye irritation.
Another lower cost option is to install wrapped fiberglass insualtion, which will cut down on the amount of fiberglass particulates in the air but not eliminate them.
You might also think about installing a radiant barrier at the roof to keep the storage space in your attic cooler in the summer.