Does the typical graph and its contents within the box come with everything one would need to mount on the bow and mount the transducer on the TM? If not, what would one typically need in order to be completely set up?

It will come with the mount that lets you mount it on any flat surface. Several mounts out there that let you get it higher. Personally, I see no benefit to having a graph on the bow if you have to spend all your time staring at the deck.
For the TM mount, you can fasten it with bit hose clamps, but a mount from Transducer Shields & Savers will keep it from being broken off when you hit a stump. Not cheap, but saving one transducer pays for it.

Most all graphs will come standard with a transom transducer. If you go with Humminbird they will offer a transducer exchange program where you can send back the transom xducer in exchange for the trolling motor transducer. This is done mainly on the DI models and a small cost will apply for the swap. Lowrance will sell you one for %50 off. Otherwise like Bob above stated it will require the transducer shield and save bracket to assist you in mounting the transome transducer to the trolling motor.