I'm completely gutting and redoing my guest bath. It sits at the end of the hallway, so it has 3 walls interior, one exterior.

As far as insulation on the interior walls, is there any benefit to doing that? If I do, should I use faceless insulation? What about a moisture barrier?

For the exterior wall, I was just going to use faced insulation.

Maybe green board anywhere near or in the entire bathroom?

In our climate, the AWB is generally on the exterior of the studs, so you shouldn't need faced insulation in your exterior walls, but that depends on how your home was built. Insulation on the interior walls helps with noise transmission and helps a house feel more "solid". If you want to do that in a restroom, you either need to install a moisture safe insulation like rockwool or put up a vapor barrier prior to wall board. This is assuming you don't have fully tiled walls with a waterproofing system already.

https://www.schluter.com/schluter-us/en_US/Shower-System/c/SS

I'm going use green board everywhere except where I'm putting tile. I'm going to tile the walls above the tub, and I'll either do hardie board with a waterproof membrane, or have the tile people put in their stuff, I forget what they use. Thanks for the input.

You really don't need faced insulation at all. It is easier to find, and you can use it if you want. If you call an insulation company they will sell you unfaced for your project. If you are in BCS, I can recommend one.

Basically the kraft paper is supposed to be a vapor ******er. Here is the science:

https://www.greenbuildingadvisor.com/article/should-the-paper-facing-of-batt-insulation-face-the-inside-or-outside

In our climate, we typically use a vapor barrier (Tyvek) under the siding to keep the wall dry. You don't want another vapor barrier inside the wall because we don't want to create a moisture sandwich.

As for the shower, you do want a water barrier under the tile to keep the wall assembly dry. I know this seems to contradict my previous point, but you have to keep the wall dry. The schluter, kerdi, or redgard system is very important for a tub/shower.

Also, AggieTaco made a good recommendation on Rockwool.

How much is rockwool 16" 48" r15 batt typically? I saw HD prices were crazy ... $50

That's good info, thank you. I guess I misspoke. I use the redgard over the backer before the tile.

That's the going rate for retail, but that $50 is for a pack of 12 of the R15 16"x48" batts.