Bring the stem and the seat to a plumbing hardware store and they should be able to help you. Bring the handles too. This all helps the counter guy.
The seat needs pipe thread sealant on the threads before you thread back in, and yes you will need to pick up the wrench in the drawing.
If you want to get real fancy, you can get a remodel plate and reinstall with a single handle pressure balanced valve. Then you not only have a valve that holds the temperature steady, but you should be good for parts for a long time to come.
I like the avatar, now you need to trim the bolts and snap on the bolt caps.