What is the best type of fabric to use to drape over an arch?

Tulle looks very nice in an arch and there is always the option to add twinkle lights and a solid material to the outside if wanted . Or you can keep it light with the tulle and more cost effective

Tulle! I think organza is similar, just a tighter knitting to it. Also, chiffon is fairly flowing (don't know if people use it on an arch, but it's what my bridesmaids dresses were made of!)

You could use tule. That would look really nice with some flowers cascading down it.