Specifically for that Swiffer thing: I got reusable fleece heads off amazon that I like a lot.
https://www.amazon.com/dp/B07H76FZ77/ref=cm_sw_r_cp_api_i_CIvWDbWFZ3HA9
For most surfaces I dry dust once with a rag and wet dust (using up all purpose cleaners before DIYing it) with a second rag after.