You want to keep the cleaning process as systematic as possible. This way you do not have to worry as much about forgetting a spot. I have found that using a checklist is a great way to keep the routine and maintain a consistent level of cleanliness.
Even if you do not have carpet in your unit, it is a good idea to invest in a vacuum. Broom sweeping will leave behind or move around hair and dirt that a vacuum would take care of on its first pass.
There are multiple places I have found a Magic Eraser to be a lifesaver. One is cleaning off soap scum on glass shower doors.
I am definitely in the camp of finding one cleaner that is good for as many tasks as possible for cleaning the Airbnb. I recommend a gentle, all purpose degreaser style cleaner that does not leave behind as neutral scent as possible.