Take all the furniture out of the room. Spread out tarps.
Sand the drywall surface with your vibrating pad sander, getting it flat and smooth.
Apply primer over the whole surface, using a paint brush to do the perimeter and using a roller to do the rest. Let it set overnight.
Use the paintbrush to apply textured paint along one edge of the area, in a line of about 5 feet. Use a roller to apply more textured paint from there, building outward from the edge to make an area of textured paint of about 5 feet on a side.
Step back and assess the area to make sure you're getting the texture consistent throughout.
Repeat the process to texture the next section of the area, alongside the first section, again using a brush to apply the paint around the edges and the roller for the rest. When you step back to look at the area afterward, make sure the line where the two areas meet looks consistent with the rest, so it forms an unbroken span of texture.
Repeat and continue, covering the whole area and frequently looking at it from a slight distance to make sure it's consistent. Let it dry 24 hours before bringing the furniture back in.