Touchless car washes get the job done using harsher detergents and cleaners then what you would typically mix up in a wash bucket.

This means whatever wax you had on at the start of the wash is probably gone by the end.

I prefer lambswool washmits and soft towels (microfiber being my choice, 100% cotton is okay). Kit Carnauba, Meguiars Gold Class or NXT wash are all good and a little goes a long way.