There are two major problems with cotton. First, if it gets wet while you're wearing it, you'll be very very cold. Wet synthetic fabric (or wool)is warmer for some reason. Cotton also takes a long time to dry. Synthetics dry much faster, which matters when you're washing things by hand. I'd go with synthetic clothes if at all possible.
Two pairs of good hiking socks are probably enough. You really only need two sets of clothes -- one to wash, one to wear. Two t-shirts, two pairs of slacks or shorts, two pairs of socks.
You definitely don't need a real towel. It's too heavy and bulky. And imagine how heavy it will be if it ever gets accidently soaked. But yes, the camping towels can be expensive. I used a bandana as a towel. It more or less works to dry off after a shower, takes up almost no space, and costs almost nothing.
I like the hydration systems, but that's a personal preference. I love my camelback. Since it can be hard to tell how much water you have left with a hydration system, I usually also carried a half liter bottle of water -- just in case.
I used shampoo for everything - soap, shampoo, washing clothes. I took a small bottle (about 3 ounces) and refilled it every few days. It worked for me.
I'd second xm on going with a smaller bag so you won't be tempted to take too much stuff. Mine was advertised as a "day and a half pack" and worked just fine for nearly a month and a half. And I saw (and envied) people with even smaller packs.
I took a fancy synthetic hat that worked for both sun and rain and was glad to have it. And, unlike straw, you can dunk it in a fountain on a hot day and put it back on wet. Very nice.
But, as you said, people surely used to make this trip with just the clothes they were wearing, a hat, some sandals, and maybe something to carry water. As I see it, everything else is optional.
Buen camino!