What aspects should one keep in mind when choosing monitor for photo processing? What about color gamut, panel types, input types, requirements for video card, different gammas, refresh rate, angle of view?
There are probably a few things you should look for. Color range is probably the most important factor, and a monitor that is at least capable of representing the Adobe RGB Wide Gamut color space (or color gamut) is important. Most professional cameras will generate images in the Adobe RGB space, while many printers, such as Epson's Stylus Pro line, support a gamut that in some areas extends beyond even the Adobe RGB space. Many photographers like to work in the Pro Photo RGB color space, which is quite a bit larger than Adobe RGB or that of most printers, and often beyond the range of most monitors. If you want the ultimate in color quality, the higher the color range the better. LCD technology on a professional screen (i.e. Apple CinemaDisplay 30" HD or Eizo ColorEdge) will produce fairly accurate representations of the Adobe RGB space, up to around 98%. Newer LED LCD technology on top of the line screens (i.e. LaCie 730 LCD) will produce accurate representations of a considerably greater gamut beyond Adobe RGB (in the case of LaCie, around 120%.)
Second, you will want a monitor that offers a high range of contrast. The color gamut that a monitor supports (such as Adobe RGB) clearly represents color range, but does not always represent the full contrast range. A high-contrast screen will be useful in representing a broader range of tones. I would look for something that offers at least 700:1 to 1000:1. Professional and top of the line LCD and LED screens generally fall within this range.
Finally, the brightness of a screen can play an important role. If you intend to place your computer in a darker area, a moderate brightness of 200-300cd/m^2 will probably be sufficient. However, if you need to place your system where bright glare from lighting or particularly sunlight might overpower your screens brightness, a brighter screen will probably be necessary. I would go for something around 380-400cd/m^2 if you have a brighter work area. Upon calibration, the necessary adjustments to correct a screens gamma will result in a lower operating brightness than the maximum brightness you may see when purchasing a screen. An ideal brightness to support accurate representation of printer gamuts is about 80cd/m^2. A very high end professional screens such as the Eizo ColorEdge CG303W or LaCie 730 are designed for an operating gamut of 80cd/m^2. Middle-grade screens such as the Apple CinemaDisplay start to loose dynamic range at such a low brightness, and operate better at around 120-160cd/m^2 in a properly lit environment.
Once you have purchased a monitor, to get the most out of it, it is important to color calibrate it. Most monitors provide a default color profile that does not accurately represent colors...often by oversaturating. Additionally, the setting in which you use your monitor changes the appearance of the light it emits, so even if you manage to find a properly calibrated monitor, it is only going to be calibrated for its previous environment, not the one you place it in. You can easily calibrate your own monitor with a device like the DataColor Spyder. There are a variety of versions of these types of devices, and they range from $30 up to many hundreds or thousands of dollars. Generally speaking, something along the lines of the Spyder3Pro @ $170 is sufficient to accurately calibrate your monitor. If you spend $1000 or more on a screen, $170 is a drop in the bucket to get the most out of your new beauty.
There are a three types of flat-panel monitors (IPS, VA, and TN) and IPS will give you the best results for photography. It's often difficult to figure out the exact type of panel a given monitor uses; here's a list.
Install it somewhere you can provide consistent lighting, and calibrate it with a hardware colorimeter.
If you are getting an LCD you will want to get an 8-bit monitor instead of a 6-bit monitor (a lot of this stuff depends on your budget, but I would say this is the minimum). A lot of LCDs are the 6-bit which have a faster refresh rate for gaming and movies.
Here's a good article on the details, quite a bit of info. One thing to also consider, when getting a good monitor is a calibration device. I use the Pantone Huey Pro, but there are several other great options out there. You'll want one that stays on and helps to compensate for changes in ambient light if you're working in a room with lots of light sources such as windows.
Color is the most important part. If possible choose a monitor with a wide color gamut, then get a color profile for the monitor.