Wrong question ... but help's still on the way.
Obviously, the few mfr's of computer monitors (screens) all produce pretty much the same thing, so recommending any monitor (which would, in effect, be no different than recommending a brand name/model) cant really be expected make a difference.
Now there is lots of advise (usually unnecessarily techno-speak oriented) dealing with this subject, little or none of which is ultimately very effective. That is because it tries to address individual problems not clearly described. Or because the advise fails to address the cause of the problem...and that last part is what is generally misunderstood, both among average users...and especially, sad to say, among experts.
However - and this is the first time this has been published! - the basic cause of eyestrain, since forgotten, was found long, long ago (I mean, years in the hundreds ago), and with it, the solution which I recommend should always be tried first...and is guaranteed to work barring some significant eye malady or health issue.
Long ago it was discovered -- I discovered it as well when computers went from white-on-green to amber-on-black [still the most eye comforting display color combination]; then from monochrome (best on eyes) to color (which, surprisingly for me, proved to be more likely to cause eye strain); then from CRT to LCD which proved no less likely to cause eye strain -- that eyes strain has virtually nothing to do with the display media (be it monitor screen or hard copy page...do you see where this is going) or with the aided or unaided vision of the user/reader.
No! What it was, is where the light is coming from; yes, that is right, and if you think of how (of the normal environment in which) eyes are naturally used, this become intuitively clear. Normally, the light (natural sunlight, but also artificial light, and in both cases more-or-less dispersed light), coming from a single direction illuminates what we are looking at. (We do not typically look for long periods at a light source...and if we did - without squinting - eyestrain would eventually ensue consistent with light intensity; but I digress.) However, in computer settings, not only is the monitor a light source as opposed to being illuminated, our eyes are also detecting light (are trying to cope with) light from different source(s) (the same which are illuminating the keyboard). So now we begin to see the true cause of strain in terms of the unnatural demands which the computing environment (just like the reading environment...as we shall soon see) places on the eyes. The typical computer monitor is situated such that the user's eyes attempt to focus while adjusting to fluorescent light emanating through the screen (in varying degrees of intensity and coloration and contrast), but must do this while also adjusting to a light source coming from a different direction in the environment...typically overhead. &or elevated above the eyes. We are aware of the monitors light (so we blame the monitor), but largely inattentive of the surrounding light (so fail to recognize that as the primary culprit) which is actually causing the problem; causing the problem by presenting the eyes with adjustment/compensatory tasks for which the are not designed and with which they cannot hope to cope without fatigue and strain. And, because we don't recognize the problem as the external light, we also fail to recognize the solutions -- in this case, the solution to eyestrain caused by reading; a solution that was first come upon in the pre-computer age (going back to the days of gas lights!) ; a solution that will also work when reading computer monitor screens.
In this regard, two "applications" come to mind, only one of which, however, provides a workable (also the best .. and least inexpensive) solution to eye pain in the GUI environment; those are: libraries and bookkeepers/clerks bills ... That is, visor bills as in cap visors.
To those fortunate enough to visit great/ancient libraries such as library of Congress, with huge spaces and 50 foot, sky lighted ceilings with massive, yet still distant, overhead lighting, one will observe on the reading tables those appealing table lamps (variously called clerk lamps, bookkeeper lamps, lawyer lamps, library/reading lamps ..., all having in common the half-tubular, green, translucent glass (nowadays sometimes plastic) shade. In such situations where close-up lighting is needed because general lighting is too distant or too weak, the table lamp with green shade serves the purpose of illuminating the page for the eyes (which does not cause strain), but also of not allowing light from the lamp itself to emanate up into the reader's/writer's/tabulator's eyes (which, in conjunction with reflected page light, would cause strain). It would appear, however, that solution has no practical application in the computing scenario.
Happily, an even simpler (and cheaper) solution, the bill (aka visor), is an eyestrain preventative which translates readily into the computing environment. Even in the gas-light (and candle) days it was found that wearing a bill will relieve the eyes of coping with incident light (light [invariably overhead light]) other than reflected light from the page) thus imposing on the eyes the exclusive, and easier, task of solely focusing on the printed/written type/script. (Even with candlesticks and sconces, such limiting of visual field [and perception) to the reflecting page served to reduce the strain otherwise induced by flame flicker.)
Concluding, and assuming your environment is typical, I would recommend you do as they did in days of yore: and keep your bill/visor/cap with visor always in reach at your work area, and never interact with your monitor screen without it on your head.
This is a policy long since adopted in our family...with no problem of spontaneous eyestrain and greatly reduced problem with fatigue since. Until the bill/visor over your eyes becomes second nature, not only will you be surprised how much more eye pleasing, you might also be surprised at how great a factor eyestrain is (had been) in overall monitor induced fatigue.
It is recommended strongly for use without exception in schools...but you cannot assume sending your child with cap and instructions to wear before computer in class will not meet with resistance; some educating of the educators might be required.
Once schools and others catch on .(perhaps establish requirements as well) maybe a boom in computing visors -- sport-/action-figure computer caps for boys, fashion computer, do-visors for the girls. And with lots of existing suppliers and stores, no ridiculous computer gear prices.