Another problem with using pure colours (red, green and blue, at least) is that it will cause a visual misalignment on the screen (for LCD-type and OLED screens, as well as Trinitron-type CRTs and plasma displays running at maximum resolution). Since only one of the three subpixels is lit up, and each pixel is composed of three vertical bars, one each of red, blue and green, pure colours will seem to shift slightly left or right compared to desaturated colours (which need to use some lit-up combination of all three subpixels).
Don't play with the white values until you see them against the final background colours. What seems glaring against a pure colour or black might just work perfectly well when set against a desaturated background. You won't know what contrast level is appropriate until you determine what the light text (or whatever) is being contrasted with. Mind you, all of this would be much, much easier if people ran properly-calibrated monitors. White should be paper-white (for relatively bright values of "paper", of course) rather than staring-into-the-sun-white. My main monitor (used primarily for high-end photo editing) is running at about 40% brightness (a little brighter during the day, a little dimmer of an evening); it's not even one of the brighter monitors on the market, and the default 100% brightness is out-of-control, eye-watering, blinding bright. I figure that people who run high-brightness monitors turned up full blast get what's coming to them (much like the headphone wearers you can hear from a city block away over a traffic background).