If a floor is particularly dusty or dirty, then vacuuming is required before washing, to avoid making mud pies. When we find such conditions, we generally use our vacuums to collect the dust and dirt, rather than a broom. This serves to reduce the amount of particles which become airborne in the process of sweeping your hard floors.
Mops spread dirt and germs. Spreading dirt and and germs around from room to room is not a good idea. So, we don’t use mops. We use microfiber floor washing pads (several per house). Microfiber collects particles up to 10x more effectively than terry cloth. These allow us to use less chemicals (vinegar or all purpose cleaner, depending on the surface) than would otherwise be required. we avoid spreading dirt and germs from room to room by changing the pads and water for each room. This is in stark contrast to other services which carry a mop from house to house (if your service does so, fire them immediately–it’s totally unsafe!).