Apply a color blocking primer and sealer to the walls, and it may be necessary to lightly sand the surface first Try using 220 grit paper.

You might ask the store where you buy your paint to tint it for better hiding of the burnt orange color, which I am thinking is a dark, reddish orange. I would suggest a pale green. This coloring will reduce the transparency of white paint.

Otherwise, you should just use a quality paint, and two coats will normally finish the job. If you need a third coat, a few 'handfuls of water will help the paint go farther, and should cover the spots that didn't quite get it with the first two.