If you are missing any items, it can effect the quality or cost of the cleaning job. Theses are my suggestions:

A good vaccuum cleaner with new bags and extra belt available.
Broom and Dustpan.
Swiffer
Paper Towels (Bounty)
Sponge(s), Rags (unwanted t-shirts or towels)
Step Stool or Similar for high shelves, if any

Laundry Soap, Fabric Softener or Dryer Sheets, Change for any coin-op machines.
Murphy's oil soap if any bare wooden surfaces
Windex
Pledge or Endust and S.S. cleaner (if you have a Stainless Steel Appliance)
Brillo or S.O.S with soap in pad
Dishwasher liquid or powder
Soft Scrub or Comet scouring powder
Mr. Clean or Lemon Pine Sol
Fantastic or Tilex