Eugene's observations

The size of your monitor is one of those things that you only appreciate when you have a larger one.  Just like dialup internet many people think they work fine with the old 19" CRT but after a week with a twin 24" IPS setup they soon realise that as a general rule, bigger is better.  Note that size is the viewable region measured diagonally.

Like all things you get what you pay for.  I well remember the headaches I frequently got from spending too long staring at my first cheap monitor.  So apart from size what should you look out for ?

Resolution is probably top of the list.   1080p monitors (that is, monitors with a native 1920 x 1080 pixel resolution) are very common, and a typical 23" screen produces fairly sharp images.  But the larger the screen the larger pixel density you will need to maintain that sharp image.  Larger densities are also good for offering the keen eyed more real estate, and those with poor eyesight space on a large monitor to enlarge text and images.

Screens are typically matte or gloss.  The former is usually best as it minimises glare - especially important when the light source is behind you.  However, if vivid colours are your thing then gloss wins out.  Anti-glare coatings will help reduce the problem if you need a compromise solution. 

The refresh rate tells how often the whole screen is repainted.  60Hz is the minimum acceptable.  Pixel response is the time needed to change from one shade of grey to another - 6 milliseconds or less will be fine for general use, gamers may prefer 2 ms rates.

Physically, make sure the movement is what you want.  Tilting around the horizontal plain is a must have, swivelling around the vertical less so.  Adjustable height is often useful.  If you really must have speakers built in then do but don't imagine the sound quality with be high fidelity.  A USB hub may be helpful if you are short of accessible ports - remember that USB 3 goes much faster than USB 2.  You will need a connector to match that of the device you will connect to so check whether you need DVI, HDMI, DisplayPort, or 19 pin analogue. 

Beyond the above you could look at brightness, contrast ratios, and colour gambits but if you're that much into it you won't be reading an introductory text such as this.  It is worth noting that the picture quality depends on the graphics card in use as well as the monitor screen - most built-in (to the motherboard) sockets will be fine for all but immersive gamers and watchers of Blu-Ray movies.  For the best quality you may want to add a discreet graphics card, but then the price tag of this project will be sure to soar.