I don't have a specific palette, and I'm afraid I don't have a great method for selecting one. You might have better luck posting your work to a website like Pixel Joint or Pixelation.org for specific critique on what you're working on (or to just discuss pixel art in general).
I'm probably not the person to ask since I never had the patience to study colour at depth. My sense of colour has been slow to develop and what I know has just been slowly absorbed over many years (and I still have much to learn!)