First, I would need to weigh the opportunity cost of performing the task myself vs outsourcing it to a service provider (laundry mat, app/service, dry cleaner). To find that opportunity cost, I would multiply the estimated amount of time that it would take to complete the task in its entirety by what I feel is the current value of my time. This "current value of my time" is an amalgamation of multiple, context specific factors (e.g. my professional hourly rate, how imminent the need for clean cloths/a specific garment is, the value & urgency of other tasks that could be accomplished). If the opportunity cost of performing the task myself is greater than the cost of outsourcing it to a service provider, then it should be outsourced.
If it is determined that the task should be performed by me, I would start by first separating the laundry into piles of like colors. Then each pile would be subjected to the following process, with each pile going through the process completely prior to the next pile beginning