How thick are the slats?

Do you mean the wood base?

A wood slat wall looks best with a dark recessed base detail. See the difference in the two photos.

Sorry Bev but I guess that's a personal prefenced thing. The dark looks silly with the side white--to my eye. The slats themselves don't look different at all. If you end it at the floor you will have to re-scribe the trim and cut back the two side walls. The thickness of both is a variable. If the trim isn't thinker than the slats it's going to look odd to end it at the trim.

Here is a very old slat installation and they do not have base but float off the floor, and ignore the fact that there is base on the other walls. Base installed over the slats will create a little dust trap at the bottom of each pair of slats. These slats conceal a door.

I like that idea. I'll have to consider it also