SSG(P) (Join to see)
AR600-55 has some of what you seek.
The rest of it will come from unit policy Corps, division, brigade, battalion

And just as importantly speak to your commander
You are after all his master driver, so his priorities are your priorities

Sorry just getting back to you, I've been retired now for 3 years but when I was at BN level the BN Master Driver was in charge of implementing a training program for the company's in that BN. He taught a trainer for each company so they could teach drivers training for their company. Don't put to much on yourself, that's why you have Motor SGT'S in the company's, delegate them to make sure the training gets done.

BN MD is to ensure unit MDs are doing the training by the book. They tell you when they are and you make sure you pop in every now and then. You are supposed to have all Army, Post, Division and BDE policies on hand with training material if needed to include routes and you put that on the training calendar or DTO.. You hold sync meetings with them, etc. Yes, at minimum it is Humvee and LMTV, everything else, the MD is supposed to be licensed on them to ensure proper training. If I don't have a Fueler on my license, I cannot train soldiers on a fueler. Hence the MDs are usually coming from support units. TO answer your question, it is the unit's responsibility to train what vehicle they have, usually it is what is in the motor pools and/or MOS based.