Using a piece of rope for the tether is fine in my opinion. They key thing is to be able to undo it, under load, at the person end in case you get trapped somewhere where you don't want to be.
Couldn't agree more. A length of line will work just fine, but make sure you can detach from it quickly under ALL your body weight. Litterally hang youself by your tether, and try and release yourself. A large snap shackle is a great investment.