Start by documenting the unit. Walk every room and take photos and video before anything is moved. That record protects you on the security deposit and gives your cleanup crew a clear picture of the job.
Next, check your state's rules on abandoned property. New Jersey, New York, Connecticut, and Pennsylvania each have their own notice requirements for belongings a tenant leaves behind, and following them before you clear the unit protects you from a dispute later.
Then schedule the cleanout and cleaning together. Hiring one crew to remove belongings, haul trash, and deep clean the unit is faster than coordinating a junk hauler and a cleaning service on separate days, and it means one invoice and one point of contact.
Finally, use the empty unit as an inspection window. Once it's cleared and cleaned, it's the easiest time to spot repairs, replace filters, and touch up paint before the next tenant moves in.