Actually, there are three main components of dust: first, dead skin cells, second, the dried feces and dessicated corpses of dust mites (lovely thought, eh? When people develop a house-dust allergy, this is usually the component they are reacting to), and the last component by volume is tiny fibers shed by clothing -- cotton is bad for this, and jeans are the worst. This is for ordinary house dust. (Incidentally, dust mites are not generally visible, except with a microscope; they are 200-300 microns long, they eat dead skin cells and live in bedding, carpets and soft furnishings. Always. Trust me on this, anything a year old or more has a good population of them.)
In the case of a new basement, on the other hand, the primary component of dust is likely to be the obvious: concrete. Elsewhere in a brand-new house plaster and plasterboard both "shed" copiously over the first few weeks.
And outdoor dust is fine particles of soil and stone dust (composition dependent on location and prevailing winds), with a hefty component of pollen and other plant material.
So it does depend on where you are.