First Q is whether you have real plaster or drywall. SR gives you nothing to nail to. Old plaster has lathe within but it might be too loose to nail to.

Me - I would use PL Premium polyurethene Constuction Adhesive and my finish nail gun. That's if the plaster is sound. Loose plaster woiuld fall righ apart so you might as well take it off.

Properly, you need the furring nailers. I'm assuming vertical beadboard... there are a thousand different styles, but 1927 usually is a Vgroove vertical with bead.. with that you will. Where as with panels you may not, and with ply it's as Piffin says.

Alter Eagle Construction & Design

I forgot to say that, the walls are plaster.

So you think glue the panels right to the wall and then use the brad nailer (that is the same as a finish nailer right?) Or glue the panels and then use a furring nailer (I have to look that one up).

I've set plastic anchors in the wall to hang shelving and such on. If the plaster can handle that it can probably handle the brad nails right?

I have to agree with the furring idea. The strips allow air to curculate behind the wainscotting and this will help to keep down warping. The old way using panels on a wall was always furred out first.....MJH

Are you going to use panels or individual strips? If you are going to use panels then just nail at the studs. I would not use adhesive. If you decide to remodel in the future then your plaster will be destroyed when you try to remove the wainscotting.