When purchasing a new computer, or even just upgrading parts, your monitor size plays a major role in satisfactory use of your computer. The first thing that should come to mind is how you will use your computer.
For instance, if you'll be using graphics programs, which may entail manipulating photos or creating design pieces, larger sized monitors are best because they provide you with a larger "canvas" to work with. Not only will you need to be able to see the image(s), you'll need to be able to use tool bars or see smaller information windows while working. If you're a big fan of watching movies on your computer, a larger screen would benefit you as well.
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Resolution, the height and width of the total number of pixels on screen plays a major factor in choosing a particular size of screen. It is possible to have two different sized monitors, but have the same resolution. What does that mean essentially? It's relatively negligible when viewing things from a few feet away, but if you need to see more detail and clarity, it would be best to get a higher resolution with a larger sized screen.
The best rule for your operating system is to display it at the monitor's 'native' resolution. That basically means the highest resolution the monitor can display. Images will be their sharpest at that resolution and easier on your eyes.
One last thing to consider is space. If you don't have room for a larger screen, grab a smaller one. Technology is better now, so smaller sized screens can provide good viewing as well as larger ones.
Size may matter in certain aspects, but it always comes down to personal taste. Find one that suits your needs with the style you're looking for and you'll more likely be satisfied with your new monitor.