Hmm. Something to think about. We've already talked about painting, but it's a weird layout. There's no break up between any of the walls. It's been suggested to book end the walls. Hard to explain without pictures.
I prefer a smooth, flat surface. Especially using individual tiles, does not matter so much using the mat style. Not having a flat surface can cause "lipping" (edges higher that others creating a lip).
If drywall is present I will go right over it. If it is a tear out/new construction I always use backerboard.
depending on the texture, you could possibly give it a tight skim with drywall mud and make it smooth (smooth enough to paint) with minimal sanding. if the texture is heavy, backer board might be easier/better.