What type of insulation under new laundry room "closet?"

I plan to build a small laundry room "closet" off of an existing kitchen. Stacked washer/dryer. The space will be approximately 3'x5' and will jut out into the existing garage.The plan is to build a "deck" out over the garage floor, since the garage floor is 15" lower than the existing kitchen floor.
What type of vapor barrier/insulation should go between the concrete garage floor and the plywood subfloor of the new "closet?" Any issues with new plumbing penetrations of existing rim joist? The new subfloor will be continuous with the existing kitchen floor. Under the existing kitchen floor is unfinished basement space. The walls in the new closet will be insulated with standard fiberglass batts. Thanks in advance.

Not sure, but keep in mind that the separation of a garage and house needs to be built with fire codes in mind.

Thanks Jim for the reminder regarding fire codes. 5/8" fire resistant drywall and firestopping are on my shopping list.

I still don't know how to install the insulation between the garage floor and the new laundry room floor. Obviously I could pack the whole 15" space with fiberglass, but my real question is where to put the vapor barrier. Should it be against the (potentially damp) concrete floor, or should it be facing the warm side of the room as I will do for the walls? Where's Dana when you need his expertise?

I'll let this reply serve as a "bump", maybe someone will chime in.