Nobody loses a deposit because the living room floor wasn't vacuumed. Deposits go on the things that are invisible while you live somewhere and painfully obvious once the furniture is gone: the inside of the oven, the inside of cabinets, the tracks under sliding doors, and the line of dust along every baseboard.
Start with the kitchen, because it's where the most money is at risk. Oven interior, including the racks and the glass door. Refrigerator interior, including the drawers and the seals. Inside and on top of every cabinet. Behind the stove if it pulls out. The range hood filter. Dishwasher interior and the rubber gasket around the door.
Bathrooms come second. Grout lines, shower door tracks, the underside of the toilet seat and the base where it meets the floor, the exhaust fan cover, and the inside of the vanity. Hard water staining on glass and fixtures is the single most common write-up we see on inspection reports in this area.
Then the things that only show in an empty unit: baseboards, window sills and tracks, blinds, closet shelving and rods, light fixtures and ceiling fan blades, switch plates, and the corners where walls meet floors. Vacuum and mop last, after all of the above has been knocked loose and wiped down.
One practical note on timing. Empty-home cleans are faster, cheaper, and far more thorough than cleans done around boxes and furniture. If you can hand over the keys to a cleaner after the truck leaves and before the walkthrough, do it. Book it as soon as you have a date, because the end of every month fills up first.