LED backlit displays offer the least amount of flicker of any current display technology. You want to avoid Plasmas as they build up the image temporally in a similar fashion to DLPs.
The LCD panel refresh rate (60Hz, 100Hz, 200Hz etc.) is actually decoupled from the backlight. So it doesn't matter if you have a 60Hz LED set, or a 200Hz LED set, the amount of flicker from both panels should be the same.
That said, many of the higher refresh rates offered today are not "true" refresh rates, and are achieved by operating the panel at, say, 200Hz, and then using a technique called backlight scanning to improve motion handling to equivalent of say 400Hz. This backlight scanning technique does
introduce flicker into the image, though it should be imperceptible to most people.
With Sony LCDs, you can decide whether backlight scanning is used depending on the MotionFlow option you use.
- The Off, Smooth and Standard options do not use backlight scanning.
- The Clear, Clear Plus and Impulse options do use varying degrees of backlight scanning. (and you should see a drop in brightness as a result)
I don't know whether other manufacturers give you the option to enable/disable backlight scanning, or what their options are called if they do. If I recall correctly, a friend's LG set does not give you the option to disable backlight scanning at all.
If you are thinking about 3D, you definitely want a set that uses passive 3D rather than active 3D. (though personally I don't think 3D is worth it) I believe that a friend's Panasonic LCD with passive glasses has the option to enable/disable backlight scanning, though you would have to check that to be sure.
And the panel is effectively always running at the highest (true) refresh rate possible. If you send it a 24Hz signal, it will run at 240Hz, 480Hz etc.