Stop motion animation relies on photographing a pose, moving something, and photographing the result to establish the next frame in what will eventually become the animation. Unlike film, though - which is shot continuously - stop motion animation is built upon a segmented time span, and this has certain implications for photography.
In order to sell the experience of continuous animation (which is what the viewer is meant to see), one must minimize any discrepancies in the environmental conditions which occur between frames. Progressive changes are perfectly acceptable, but disjointed ones such as having the first frame be dark, the next one bright, and the third one dark again need to be avoided at all costs. The first step towards achieving this is to shoot in a controlled environment (with no natural light); the second, is to make sure that the camera itself does not betray you.
While one could theoretically use any sort of image capturing device for stop motion - from webcams to the cheapest point-and-shoot camera or smartphone, right up to the most expensive professional SLRs - there are a number of factors which make some cameras better suited for this than others.
1. Manual controls
By far the most important factor to consider is having complete manual control. Low end cameras tend to include only automatic (or semi-automatic) exposure settings which - while good enough for one-off photos - are not suited for stop motion series. The problem with automatic controls is that the camera might decide (by itself) to change settings partway through your animation; and given that animation tends to involve changes to the subject of your photo, this is in fact quite likely to happen. The automatic camera is only trying to get the best photo in each frame; but what YOU want is to get consistent photos in all the frames which belong to one animation.
As such, your main priority should be to get a camera which has manual exposure controls (F-Stop and Shutter Speed), and manual focus. Most SLRs will have this, as will some higher end point-and-shoot cameras, but some webcams also have this, as do smartphones with recent versions of Android (5+) or iOS (8+). If obtaining a camera with manual controls is absolutely impossible, then you might still be able to reduce exposure discrepancies in post (using image manipulation software), but keep in mind that the results of this will never be perfect.
2. Remote control and previewing
While not absolutely necessary, the ability to remotely control your camera is extremely useful when shooting stop motion. One reason is that by avoiding direct contact with the camera, you minimize the chances of accidentally moving it while shooting. Keep in mind that pressing the shutter release button (or screen, if that's the case) normally requires a bit of force, and even if the camera is attached to a tripod, there is still the risk that you might rock it slightly while doing this; and a change of even a few millimeters in the camera position is enough to ruin your animation sequence.
Previewing is another function which is extremely useful to have. Most cameras which are equipped with a display will allow you to browse through your photos, but - besides the aforementioned risk that you might move the camera while operating it - this won't really give you an accurate representation of how the animation will play out at its intended framerate. Dedicated stop motion software, however, allows you to do just this while adding x-sheets and other useful features which you would certainly appreciate while shooting.
Simple - wired or wireless - camera remotes will help you with the first issue, but in order to get the most out of your camera, the ideal setup is to connect it to a computer or tablet running dedicated stop motion software. Smartphones can also be used as remotes (either through Wi-Fi - if your camera supports it - or else through an OTG USB cable) but their smaller screens make them hardly ideal. For A Shroud of Silence the camera was connected via a USB cable to a PC running Animator HD software.
3. Lens choice
If your knowledge of photography is minimal, then a fixed lens camera is probably good enough to begin with. Having the choice to change lenses, though, will obviously open up your range of expression and avoid some of the pitfalls of a single lens. I strongly recommend reading up on some basic photography and film theory even if only to understand the tools you're working with. Considering the size of stop motion puppets and sets, it really is extremely useful to understand concepts such as Depth of Field (which affects the amount of blur you see on elements which are out of focus) or Compression (how perspective is affected by different types of lenses).
Understanding photography does not necessarily mean that you will afford to use different lenses in your short, but at the very least it
will help you understand your limitations, and any possible workarounds. A Shroud of Silence was shot with a single Tamron 55-200/4-5.6 lens
(50 EUR new) attached to a Canon EOS 450D camera body (60 EUR used). These were chosen on the grounds of cost, but the combination was far
from ideal. For one thing the APS-C (x1.6 crop factor) camera sensor turned the lens into a telephoto, and the resulting compression essentially
flattened all shots; this severely limited my mise en scene. Also, the F/4 rating did not provide the kind of depth of field I would have liked
for some shots - a faster lens (e.g. F/2) would have helped. On the plus side, though, the zoom lens facilitated easier camera placement than a
prime would have.