Seconding Land’s End Towels. They’re wonderful.

After talking to some folks who are also dust-sensitive and had similar requirements we did (cordless, lightweight, etc) we settled on a Tineco A10. Available at Walmart and with a price tag around $100, we’ve really been impressed so far. We considered getting one of the higher end models, but this fit our current needs best. (Their website is a bit clunky if you go looking there, but it’s functional.)