Martin -
Like everyone else, I rinse mine in PhotoFlo (diluted with twice as much distilled water as recommended by Kodak), and then hang them by a corner, slightly off level so that any drips drift toward the lowest corner.
For years, I just hung them from hooks on the shelf over the sink in my darkroom, walked out and closed the door, and didn't come back for several hours. A couple of years ago I built a drying cabinet that allows me to continue to work in the darkroom, raising all kinds of dust, while keeping the negatvies pristine. Air is drawn into the cabinet by a small fan through an air filter, and then passes through a second filter before entering the top of the compartment where the film hangs, flowing down over the film to an exhaust vent at the bottom. I have a 200w light bulb that adds heat to the process to speed up drying. The cabinet is tall enough to hang 36 exposure strips of 35mm film.
I used a scrap of Closet-Maid wire shelving as a rack to hang from in the drying cabinet. "S" hooks are attached to the shelving, and the hangers attach to the hooks.
Hanging clips are a problem - there are some good ones out there by they are hard to find outside the speciality stores in large cities like NYC. I picked up a few at flea markets, but you never seem to have enough, and the price of purpose-made hangers offends my sense of what is reasonable.
There is an old tradition of using clothes pins, but I was always afraid that wooden clothes pins would eventually become contaminated. Instead, I found some plastic clothespins at a "dollar store" that work just fine - they have serrated teeth that grip the edge of the film, and after heating screw-eyes with a blow torch, I was able to insert them into the handle end to permit hanging from hooks. (Hold them with needle-nose pliers while heating and inserting into the clothes pins.)