I take it you had no issues with CRT monitors?
If you only have issues with LCD monitors, then there could be several reasons or combination of reasons why you are getting migraines.
1. Resolution is too high, thus causing text to appear small. Possible solutions are:
a - Increase DPI settings in the Advanced Settings within Display Manager
b - Lower resolution of monitor, makes text larger and easier to read, but not as sharp.
2. Brightness and Contrast can be too high causing eye fatigue.
3. Staring at screen for too long, take a break once and awhile.
4. Does florescent light bother you (like in an office environment)? They flicker extremely fast and looks like constant light to everyone. But this very fast flickering may give migraine to an extreme small (nearly non existent) population. If you are then you may want to look at a monitor with LED backlight; many times referred incorrectly as "LED monitors". However, LED lights flicker as well...
5. Nearly all inexpensive monitors use TN panel monitor which uses a process called temporal dithering and is somewhat similar to point #4 regarding flickering. Without going into the specific aspects of TN panel technology, simply stated TN panel monitors rapid flash between two colors to create a 3rd color which the LCD panel cannot produce without this so called temporal dithering.
For example, say a TN panel monitor cannot produce the colors purple (TN panels can only create 256k actual colors). Purple is a combination of Red and Blue, thus in this case the monitor will flash (or flicker) very quickly between red and blue so that your brain will perceive solid purple. Temporal dithering allows TN panel monitors to "blend up" to around 16 million colors.
You may need to avoid TN panel monitor and look at other panel technologies which are generally more expensive. Those panel panel techs are PVA, MVA and IPS which can product up to 16.7m without using temporal dithering. Currently e-IPS is pretty popular because it is not excessively more expensive than TN panel monitors.
Example of e-IPS monitors includes:
24" HP ZR24W
23" Dell U2311H
I really don't think 120Hz monitors will help because they basically have half of the screen refreshing at 60Hz and the other half at 60Hz as well. because the two halves of the screen are being refresh at the same time these monitors are considered to be "120Hz".
5ms response time shouldn't make much of a difference for office work since it measure the ideal time it takes the monitor to change colors of pixels on the screen. If the color doesn't change then the response time is basically 0ms because the monitor does not have to change anything that it is currently doing.
Example, you are using Excel to create a spreadsheet. You simply launch it and load whatever spreadsheet you are working on and let then just let it sit and do nothing.
With a CRT monitor, the screen is constantly refreshed as the cathode ray constantly redraws the screen from top to bottom.
On an LCD nothing changes at all, pixels do not change unless there is a change in color somewhere on the screen or when you start typing in a cell. In areas of the LCD screen that doesn't change, the response time is 0ms. However, there is the flicker of the florescent or LED backlight and if you are using a LCD monitor with a cheap TN panel, then the monitor is most likely using temporal dithering somewhere on the screen and that would be subject to response times.