Insulation, Radiant and Vapor Barriers - New? Garage insulation question

My ranch house is located in north central OH and built in the 60s. There is a 2x4 wall separating the two car garage afrom the home. The garage side is sheathed with Gold Bond R1.32 fiberboard and the interior side is rocklath with a plaster veneer finish.
I want to remove the dark fiberboard, insulate with R13 batts and finish with painted fire rated drywall.
Do I need a vapor barrier/retarder?
Would I use a continuous plastic sheet covering each bay and over each stud installed from the "open" garage side? Or would I use a Kraft faced product with the paper against the interior?
The garage will not be heated.
I appreciate any comments and/or suggestions.

Vapor retarder will face the heated side of the wall. Batt insulation that has a vapor retarder attached can be purchased.

Oddly, the guy at Lowe's suggested a 4 mill barrier against the living wall (and around the studs) and then a batt with the Kraft paper facing the garage.
I discovered yesteday that the backside of the rock lath has a foil backing.
Should I just staple the paper backed batts into each bay with the paper facing the garage and not worry anymore about it or slit the paper?

Sounds like he's having you create a situation with a vaper barrier on both sides of your insulation.

Doesn't sound like a good plan...