I take my clothes organized into Rimowa shirt bags, which are made from the slippery interior lining material of the Rimowa cases. The are colour-coded, zippered, and compress or expand well, as needed. They pack fast when on the run, and very well.
Laundry:
Unfortunately, this include a suit, slacks, tie and shirt. Sometime two sets. Casual clothes are a rarity. So those items have to be dry cleaned during any business travel. I try and negotiate something with the laundry service of my hotel. In some countries, the actual stated time in and out is hardly the reality. There have been occasions where, after checking out in the morning, I almost missed my connecting flight while waiting for my late dry cleaning to arrive.
Personal laundry I do myself. I do not like to collect or travel with laundry that needs to be cleaned. It is un-hygienic, and could be anti-business. So included in my travel kit is a medium sized zip bag of Persil-Vernel laundry soap, which indirectly gives the luggage a little clean fragrance.
As mentioned above, most hotels offer washing machines today. So grab your clothes and zip-locked soap, take your tablet or laptop, and go do your own laundry. As I sometimes am working a straight 10-13 hour day, I have to add an hour and half on top of this. In that case, a cup of Yoghurt, etc. picked up from the morning meal, may be dinner.
Hotel drawers and closets:
Over the years I know where I am staying, and my hotels of choice are clean. But that does not account for the person(s) who previously used the same room.
Upon arrival, I always purchase a bottle of Isopropyl (Alcohol 71-91%) at a pharmacy, and spray-mist the drawers and closets, full strength, first. Spray, wipe, discard. Just takes a few seconds. I can also use this for cuts, abrasions, and even as bug repellant. I just returned from a month in Brasil, and it really is effective, even in the hot, tropical Nordeste. By the time I got to the south of Brasil, it was fleece-time: 12c and cold.
The laundry mesh bags are a good idea, but they have not worked very well for me. My clothes come out more wrinkled than they should. So I just have a small laundry bag with a pull tie, also from Rimowa, and do it nightly.
Over the past few decades of international traveling, I have learned to wash everything, clean out the luggage completely, and spray-mist the Isopropyl inside when back home. Never a problem as a result.
I hope this is helpful.