I've had the best luck with the holding power if a Tap Con screw. I predrill the wood then hole it up to the wall and drill through the wall with a Bosch Bulldog hammer drill. I drive the screws with a Ryobi impact driver.
Personaly I install the foam board to the wall first with constrution adhesive and install the slats after. I use strips of Advantech not 1 X 4's because they tend to split when the screws go in.
I install a 6" wide piece along the bottom first, 1/2" up off the floor, then a 4" wide piece across the top, last I install the slats every 16".
The bottom piece is so there's a good place to install the baseboard, and up of the floor so it will not wick up water.