Hi Victor,
I travel a fair amount. I have the same requirements and add that that my clothes need to be "business casual" for the times when I'm on the clock or out of respect when visiting religious or political buildings as a tourist.
When I traveled to India this winter. I went with a wear one wash one strategy, this worked wonderfully although the temperatures were cool, the air was damp, and my <$10 hotel rooms didn't have climate control. There were a couple days where my clothes were slightly damp when I put them on, but were dry after wearing them for an hour or so. If this would've bothered me, I could've gone with a third change of clothes. It didn't so I don't feel inclined to change my routine at any point in the near future.
Here's my washing routine, at the end of the day, I'll wash all of my clothes in the hotel sink, using the complementary shampoo as the detergent. I'll fill the sink wih soapy water and start off by washing my shirt and pants first, t shirt next, underwear and socks last. If I'm covered in dust and mud from the day, I'll change out the water any time it starts to look murky. Typically I can wash my clothes with one sink full of soapy water and another with fresh water.
I dry my clothes by wringing them out the best I can, roll them up in a towel, step on the towel to get more water out, shake, and hang dry over night. In ideal conditions, my clothes are completely dry in less than 24 hours. In India this winter, it took a bit longer due to how cool and damp it was.
Here's what I wear from bottom to top:
Shoes Doc Martins. Leather so ok for business casual. Bouncing soles are comfortable to walk in for hours at a time. Durable as I tend to lose my Docs before wearing them out. I've had my current pair since 2007 and they still have life left in them.
Socks: Wright coolmax double lined gray socks. I wear the ankle high white version of these hiking. Dry fast and I never get blisters, They are always dry by the next day.
Underwear: Underarmor Lycra boxers. Dry fast and are comfortable.
Pants: Kuhl Revolvr. These are a nylon/cotton mix. No surprise that my summer weight BDUs I wore in the Army were a nylon/cotton mix as well. They dry incredibly fast, are very durable, comfortable to wear, and look nice. Even at home, I never throw them in the dryer. In ideal conditions, they hang dry within 12 hours. Also, the side pocket is perfect for carrying a Sony RX100. More on that in the photography forum.
T shirt is a nylon/Lycra mix I bought from Duluth Trading company, This is also my hiking shirt. I've had problems with polyester mix shirts stinkining after a while and I've had good luck with Nylon so I try to stick with that. This is a loose fitting and long t shirt. It never comes untucked and the black version fine to wear by itself if I felt so inclined. My tattoos are visible through the white version so I typically just wear that as an undershirt.
Eddie Bauer 100% cotton and wrinkle free button down and collared shirt: this is a case of buying quality less often. Not all cotton garments are created equal, as is the case here as EB's shirts are a step above the competition. When I wash them in the sink as described above, they are almost fully dry by the next morning, and 100% dry by the following evening when I have to wash my other shirt. I can't say that they are 100% wrinkle free, but close enough that whatever is there isn't noticeable.
Marmot Precip et al: I just bring a cheap poly lined rain jacket. This is all I need for thermal regulation down to freezing and as a rain jacket.
Edit: typical typos and occasional Klingon word thrown in for good measure when typing on my iPad. For reasons unknown, I have a hard time scrolling up after typing something on BPL.