I like 2 or 3 cleaners, less time restricted at home. Some will say you need to watch valuables more.
Deep Cleaning: EVERYTHING is moved, touched & cleaned. Costs twice as much.
Refrig: Jus ask them to include.
Rugs: Up, out & beat. Yepper.
Dusting.....yes, but the cleaners should see & understand your collection first.
Supplies: Their supplies unless you have special expectations. Use your own vacuum.
Tipping: Not every visit. Special times.
Bottomline..............have cleaners over, lay out personal expectations, get pricing.
