You can try different neutral shades, of course, but this isn't the time for experimentation. Remember also that neutral shades can create the illusion of larger rooms. Your prospective buyers won't be able to envision their belongings in your home if they can't see the floor. So you've got to clean it ruthlessly. Have the carpets professionally cleaned, throw away as much clutter as you can, clear off your shelves and organize your closets.
Excessive clutter creates stress and turns off prospective buyers.
Imagine your desk at work, covered in paper. It looks like a tornado just ripped through the room. So create as much breathing room as you can, and clear as many objects d'art out of the way as you can. If you own any conversation pieces that are an acquired taste, you may want to store those away temporarily. With an upcoming move, you needed to throw things away, anyway.