I want to make a stop-motion animation but am confused, which camera to use, a digital camera or a SLR? And what is the best brand to go with? Any suggestion will be highly appreciated! Any brand or model suggestion will greatly help me in my decision making!
You're going to want a camera which allows full manual control, because automatic exposure settings might come up differently from shot to shot, ruining the flow of images. And you're going to want to manually focus for the same reason. Any digital SLR or many high-end digicams will fit the bill here.
Since video is usually much lower resolution than given by still cameras, that's not much of a concern — any camera will do, and will probably have high enough technical image quality. However, the higher-quality still images you can take, the nicer your final result. For this reason, it's probably a good idea to choose a larger-sensor camera — either a digital SLR or one of the newer "mirrorless" cameras. Selecting a model with interchangeable lenses will give you more flexibility in finding a "look" that's right for your film.
If you do get a DSLR, it's probably best to get one with "live view", the feature which lets you compose on the rear LCD screen rather than the viewfinder. And, DSLR or not, a model with an articulated rear screen will make it easier to position the camera where you can both get the right shot and still see the screen, without contorting yourself into a weird position.
The short answer is like David Rouse said in his comment: pick your software first, then pick your camera off the compatibility list. Stop Motion Pro, for example, supports a variety of webcams, video cameras, most Nikon and Canon DSLRs, and some Canon compact cameras.
I recommend if you're just starting out with stop motion to get a good webcam like the Microsoft Lifecam to try out with your software and learn how to use its features and explore stop motion creatively. Get some lamps/torchieres/flashlights and experiment with lighting. Once the quality of your camera becomes a limiting factor, for example because you want less noise, richer colors, shallower depth of field, more resolution, more sophisticated lighting, more control over shooting parameters, or a wider range of focal lengths, that's a great time to upgrade to a Nikon or Canon DSLR.
Note that at least currently, DSLR brands other than Nikon and Canon don't appear to be well-supported by stop motion software. I haven't seen any supporting mirrorless or bridge cameras, and only a very small number of point-and-shoot cameras are supported. As such you're pretty much forced to make the giant leap from $100 webcams to $1000 Nikon/Canon DSLR kits.
We make Dragonframe stop motion software, and I can tell you that the Canon EOS cameras with live view are used by about 85% of our customers, for good reason. The live view on the Canons is large and clear and makes it really easy to see what you are doing. Also, the live view has "exposure simulation", which means that as you change your exposure settings in the software, the live view adjusts to show you what your final image will look like. Most of the Nikon DSLRs with live view do not have exposure simulation, and the live view is relatively small and compressed. Both of these camera types can be used with the software with just a USB connection, which is not true for most other cameras, because Canon and Nikon do a good job of providing libraries for developers to integrate with.
There are lots of ways to shoot stop motion with any camera, but almost any professional stop motion animation that you see (such as movies, commercials, tv shows or music videos) is shot with dedicated software and tethered cameras. It just makes the process much more enjoyable and precise.
When using DLSRs for stop motion or animation, you will be activating the mechanical shutter which will have a life of 100,000 to 300,000 shots, depending on the quality and price of the camera. Although this is a large number for stills work, at 24 frames/sec it is only 70 to 210 total minutes of footage. Dedicated video cameras (and DSLRs in video mode) do not use the mechanical shutter, so this does not become an issue. As far as I know, DSLRs do not have a single-shot video option. Fully electronic global shutters are being developed which may change the equation.
However, there are advantages to using DSLRs: the larger frame size allows more framing and pan/zoom options in post, the higher resolution allows for 4K movies (assuming you have the software to edit it), it's easier to tether, etc.