I purchase the Grime Boss Dusting Cloths to dust with. I have very bad allergies and these dusting cloths help a lot with capturing the dust instead of just spreading it around or throwing it back into the air. The dust actually clings to the cloth (you'll never realize how dusty your home becomes until you use one of these cloths to dust with and you actually see the dust your furniture collects in just a few days).
These cloths can be used on a floor sweeper or just with your hand. I use them as dusting cloths with my hands since all the rooms in my home are carpeted. They come in packages of 16 and are 8 in. by 11.5 inches each. The price is very reasonable as well at about $2 a box. They are also unsented which also helps with allergies as some cleaning products can affect my allergies just from the scent they have.
These cloths can be used on anything in your house. From your ceilings and walls to the floor or you electrical appliances and furniture. And when you are done they are disposable.