Often more than 1 photograph is involved. A release can also cover a date range. If it's just one photo, yes a copy of the photo the release applies to handy to have. If it's multiple photos, it's a good idea to attach a list of the image file names to the release.
A photocopy of the person's ID is always nice, but their contact info has to be on the release regardless.
Model release law varies by state. Model release law is not as cut and dried as say, traffic laws. Often the only correct online answer is, "It depends". Do not rely on legal advice you receive online. Make an appointment to consult a qualified attorney, certified to practice in your state.
I highly recommend the book: A Digital Photographers Guide to Model Releases by Dan Heller.