I have always used the same soap that I use for hair, body and laundry - a bar of toilet soap, and Dove is the most common in the shops on the Camino. Sure your clothes get to smell of toilet soap after awhile, but that's nothing to stress about. I didn't find anywhere the small packets of soap powder you can but anywhere in Asia. It's a pity the albergues don't make up small quantities to sell sufficient for one or two washes.
Cotton tee shirts are slow to dry, so trekking gear is much the best, and I have found the best to be Iceberg - no odour, quick to dry, warm in the cold and cool in the heat. Iceberg are made from Super Fine Merino wool, and although expensive, they are a good investment. Last year in late October I had snow and the 10 days of incessant rain, so drying was a problem, and the utmost luxury for me in Santiago was to wash and then wear clean and dry clothes. It was bliss. But that was after 5 weeks of no rain, and the year before with a few very short showers
Buen Camino David