- Edited
There are many ways, I recommend you read the docs or some other text about shading.
For starters, use lambert and maybe disable specular. If you don't want shading you can use unshaded or disable receive shadows in material.
You may still want ambient light, since quake used baked shadows.
And Color correction should be linear.
Check the options in your material and in world environment node.
An emission texture is another alternative, but it could end up looking too bright.
You can't reserve colors in a palette, if you use unshaded the colors will be the ones in the Albedo texture, but any calculated color will be in 24-32 bits, and that's because of modern hardware. You could however use a postprocess shader to reduce the number of colors through an algorithm, but a palette of selected colors would be too computationaly expensive, think of, tones in a "curve" instead (10-20-30-40 / 8-16-24 / 3-5-7).