Today I'm colour proofing...... But I have to calibrate my monitor first, to ensure that what I see on it, is a close representation of what's actually in the files.....
Most people choose 'native white point', but that may result in the monitor being too cool in tone. The only way to confirm your monitor is calibrated, is to compare it against an icc profile verification print - essentially a file that has been accurately measured and is guaranteed to be close to the file it was created from. I put this file under a daylight viewing booth (as shown below) and compare it with the source file it was printed from, with proofing switched on in Photoshop. If the 'perception' is that they are similar, then I've got the monitor calibrated & profiled well.
For essential colour accuracy, one must use a daylight viewing booth to confirm the profiling of your monitor. If the print target does not match the monitor - then the calibration / profiling is off. You also need to have a torch and an Icelandic Puffin in your studio too :-)
On a side note - daylight viewing booths such as the one I use from GTI have a colour temperature of 5000k. But there's more to it than just assuming that if the viewing booth is 5000K, then my monitor should be set to the same colour temperature. This won't work. GIT have an article that explains what 5000K actually means if you really need to know this stuff, but for most purposes, you'll find a 5000K viewing booth will be comparable to a monitor running at a temperature much higher than 5000k. (If you put your monitor down to 5000K - it will go seriously yellow and it definitely won't match your viewing booth at all).
For me, the most critical aspect is the neutrality of the black and white tones. In the icc profile verification print you see above, there is a monochrome section in the top left of the file. If I have the monitor white point set too high, the monochrome picture may appear too cold (it should theoretically go blue but some monitors don't - see below for more on this). Conversely, If you have the white point set too low, then the monochrome area will look too warm on the monitor. By fine tuning the white point of my monitor (through the calibration software I use) I can get my monitor closer to what I see on the print. This is an iterative step that I do until I find the right white point.
Lastly, as mentioned above, it's easy to assume that computer monitors should become bluer (cooler) as their white point is increased. This isn't always the case. Some monitors may go either green or magenta when their colour temperature is turned up too high, I find that my Eizo goes a little green. Apparently setting the white point only alters the blue to yellow colour axis and not the green to magenta tint.
So If you do find your monitor is going a little green or magenta, then you may have to compromise and stick to the native white point. I would suggest however that you experiment. For me, I found moving my monitor down to just below 6000K seemed to work nicely but your findings may differ.