Fabrics are constantly deteriorating, even when you can't see it, and releasing dust into the air. People with dust allergies are often told to try to keep their homes as fabric free as possible - no carpets, few rugs, no curtains/drapes, leather or wooden furniture, etc. To reduce dust build up, I would eliminate extraneous fabrics - curtains/drapes, decorative pillows, throws, etc come to mind - and when replacing furniture go for wood or leather pieces instead.
Vacuuming - vacuum first before dusting. It kicks up dust which will just settle onto your nicely dusted areas, so you want to vacuum first. Always prioritize vacuuming as one of the first things to do when cleaning, or the thing to do most frequently, as a dirty dusty rug or carpet will constantly kick up particles as people and pets walk across it.
Air filters - some people swear by air filters which can reduce dust loads in a given room. However, a nice one can be costly and you have to deal with the white noise and increased electrical usage.
Pets - instead of forgoing pets completely, commit to 5 min a week to de-shedding or brushing the pet. Seriously, our furball load has noticeably improved since I started brushing our dogs on a regular basis. The sheer amount of hair that comes off them is astounding. Also, think of banning pets from certain areas of the house. If you don't let your dogs upstairs or in the bedrooms, that means the rooms will stay cleaner longer.
Paint - always go with an eggshell or glossier finish rather than matte. Easier to wipe off scuff marks and smudges.