Well, as a result of the rot and the plumber having to demo the concrete barrier holding in the shower faucet, I had to learn--quick!
I actually ended up doing a bang up job (brushing my shoulder off). I ended up mounting both drywall and backer board. I used drywall to fill in the space where the medicine cabinet used to be, and Hardibacker Backer Board around the tub (waterproof surface which is resistant to mold).
Here's where the medicine cabinent used to be:

And here is the area around the tub:
