The color mapping is a function of how the displaying software wants to do it. The traditional technique assumes a grayscale mapping with lowest = black and a fixed upper value such as 255 = white because that's how the hardware operated. However, these days it's a virtually free operation to map an input range into any set of colors you like (including the rainbow hue-based scale preferred by some groups). Generally speaking, though, the DEM itself is usually mapped with real-world units (something like a 0 value in the DEM is 0 meters altitude, 1000 in the DEM is 1000 meters above sea level, -1000 is 1000 meters below sea level, etc.) in the case of 16-bit data. 8-bit data has no particular standard because it has only 255 possible levels and most DEMs need more than that.

The Natural Earth series are very nice dataset. Tom Patterson does excellent work. It's got all the holes cleaned up and some of the worst errors removed. The main texture maps are also an excellent resource for coloring as long as you keep things at roughly the same type of climate.