We recommend Bona floor cleaner to use on your vinyl floors (tile/laminate or the wood cleaner is okay). Avoid any cleaners with wax or "shine" agents.
Use a high-quality, non-toxic floor cleaner (like Bona) with a soft mop to clean your vinyl floors. You may also use any product that is safe for vinyl.
Avoid using any cleaners with wax as they will leave a film on your floors. You also want to avoid using any products with a "shine" agent because that can build up over time, attract dust and dirt, and become very difficult to remove.
Use a vacuum that is suitable for hard surface floors.