tl;dr
- Use only LCD panels from manufacturers being certified as using truly flicker-free technology.
- Ignore manufacturer claims and ignore labels on boxes, as they may be false.
Examples of such truly flicker-free monitors at a budget price with full-HD resolution:
LCD monitors may or may not flicker
Many, if not most, LCD flat-panel monitors produce flicker.
Older LCD monitors used fluorescent tubes. Whether driven by magnetic or electronic ballasts, all fluorescents flicker, by their nature. Avoid this entirely.
Modern LCD monitors use LEDs are used as backlighting. Ideally, these would perform with no flicker at all. But real-life is not always ideal.
Pulse-width modulation → flicker
Unfortunately, must manufacturers save a tiny amount of cost by using a technique known as PWM (pulse-width modulation) to providing dimming. This technique omits the circuitry that ratchets down the amount of electricity to naturally dim the LEDs. Instead, these manufacturers rapidly turn the LEDs off-and-on, off-and-on, off-and-on. If the LEDs spend half their time off and half the time on, then the brightness appears to be halved, for example. Unfortunately, the user is now staring into what is effectively a disco-like strobe light (not good).
While the conscious mind may not notice this flashing, many of us are indeed sensitive to this flicker. This results in headache, migraine, and so on. Personally, I suspect everyone is impacted even if perceived subliminally as “stress” or “tired eyes” without recognizing the cause.
The solution is to avoid any display using PWM. Unfortunately, there are unscrupulous vendors who label their product as "flicker-free" despite using PWM. There is no regulation or industry control over the term "flicker-free".
Flicker-free certification
So the only sure solution is to use a monitor that is certified as being truly flicker-free.
BenQ
One vendor that does not use PWM and is certified as flicker-free is BenQ. They offer a wide-range of monitors from budget-value to business-office to photographer-color-accurate to gamer. All their monitors are flicker-free. I use a 32" 4K BenQ monitor, but they offer budget-priced full-HD (1080) monitors as well.
They are certified by a German & US company, TUV Rheinland.
Eye-comfort = low-blue-light
"Eye-comfort" usually refers to the monitor offering a mode where blue-light is suppressed. Certain wavelengths of blue light are thought to mess with our circadian sleep cycle, and therefore avoided in the evening. This blue-light issue is unrelated to flicker.
For example, Apple offers this mode on Mac computers and on iOS devices, calling the feature Night Shift. This feature works only on the built-in screens. So if you want the same effect on your external monitor, you must buy a monitor with this capability built-in. You will need to manually enable/disable the low-blue-light mode on the external monetary by pressing its physical control buttons.
Beware: Colors are altered. Since shades of blue are suppressed, of course the colors are no longer true. Within a very few minutes, your eyes/brain adjust. So generally you will be unaware of the color changes if just casually browsing the web or typing email. But you cannot do high-quality photo-editing or video-editing with this mode enabled if you need accurate color portrayal. And you should not shopping for any products with just the right shade of some color while this low-blue-light mode is active.
Again, this low-blue-light feature has nothing to do with flicker. Two separate, orthogonal issues.
A quick check shows that most all the recent models of BenQ monitors recommended above offer this mode. They provide this page and this white paper explaining these issues.
The same TUV company provides certification for low-blue-light, just as they do for flicker-free.