Buying plasma is the problem.
CRTs worked by updating the whole screen at 60Hz. This caused a visible flicker, but your brain could tune it out after a while as it was constant.
Plasmas work by flashing the pixels on and off rapidly, at varying rates, to create shades.
Due to their larger size, and because different areas of the screen are flashing on/off at different rates, I find flickering to be visibly more distracting, and cannot watch plasma displays for long before getting a headache. Because it's constantly changing, your brain can't adapt to it.
LED screens produce a completely stable image. The screen illumination (LED lights) is completely independent from drawing the picture (the LCD panel) and so there is no flickering.
Some higher-end LED sets do use what they call a "scanning backlight" (many 240Hz+ sets use this) which does introduce a flicker, but it is at a constant rate (like CRT) however it is at a much higher rate, so there should be no perceived flicker from the screen.
With my Sony screen (HX900) changing the motionflow options can enable/disable this scanning backlight. The "smooth" options keep the backlight constant, and the "clear" options use the scanning backlight.
I feel that the picture is generally better with it on (sharper motion) but if I'm tired or feel a headache coming on, I'll disable it. There is no visible difference on the screen (though I can tell it's changed if I wave my hand in front as there's a very slight strobe effect in a dark room) but it's definitely more relaxing on the eyes.
What I must stress though, is that if you get an LED screen (don't get a regular LCD, they now strobe the CCFL tubes) you must turn down the backlight to a comfortable level for the lighting in your room. Too often I walk into people's homes and they have the picture up at full brightness and they complain about getting headaches after watching their new screen for a few hours. They think the problem is the TV, and not the fact that it's blindingly bright. Just because it can put out a bright image, doesn't mean it should.