I used to get silk, but now I just usually get synthetics.

The best silk ones are not really sheer but just a little bit "nubbly" instead.
It is hard to describe but they are a bit thicker than sheers and the surface is just slightly rough.
I think another name is washed silk or raw silk.

Edit: Sorry, to compare them:
The silk is not as absorbent as the cotton, but it is a lot stronger, dries faster, rinses out easier and it does not absorb stains the same way. It does scrunch up into a smaller package

Cotton is cheaper and easier to get. Cotton is also a bit cooler when damp and when dry is good as a pot grabber. Some people I know put a bandanna under their hat so it hangs down the back of their neck. It prevents sunburn.

The synthetics are ok and quite strong. About the same as silk, but absorb very little water and make really poor towels, but they do rinse clean so easy and dry so fast that they are still handy.
I buy them from thrift stores which sell them as head scarves, get the biggest you can.
I find them handy for trail marking and tying stuff up too.