Welcome to the forum.
As mentioned, there are various ways to get 'stabilization' in a camera system. If we are talking about SLR type digital cameras, then there are two main types; in-camera and in-lens. Canon & Nikon have put the stabilization (IS and VR respectably) into (some) of their lenses. They say that this works better, but it also means that you have to buy it with each lens that you buy. Other companies like Pentax, Sony, Olympus etc, put the stabilization into the body and thus it will work with any lens attached.
Now, lets look at what this stabilization does. It helps to steady the camera/lens against the small movements that happen when we hold the camera while shooting. This helps to get somewhat sharper photos of things that aren't moving. How much does it help...well, they usually say that it's between 2-4 'stops'. So for example, if you could normally get a sharp shot with a shutter speed of 1/200, you might be able to get a similarly sharp shot with a shutter speed of 1/50 to 1/12.
So it does help, but it's not going to be a cure for low light shooting, where your shutter speeds may need to get even longer.
Also (this is the big one)....none of these systems will help if your subjects are moving. They only prevent blur from camera movement, not subject movement. For that, you need a faster shutter speed...which is the same cure for preventing camera shake blur. So rather than looking for a good stabilization system, you might be better off looking for a set up that will allow you to shoot with the fastest shutter speeds that you can get away with.
Shutter speed is one of the three elements of exposure, so you would need to look at maximizing the other two...ISO and aperture. So rather than getting a camera with a typical 'kit' lens, which doesn't have a very large aperture, you might look at getting a lens with a large maximum aperture (50mm F1.8 is an inexpensive (thus popular) choice in both the Canon & Nikon systems). Next you could look at ISO....newer, more expensive and 'full frame' DSLR cameras can go to higher ISO settings with less penalty (digital noise) that older, cheaper camera...especially point & shoot type cameras.
So by using a higher ISO and a lens with a larger aperture, you could shoot with faster shutter speeds, which would mean sharper photos.
Of course, if you are going to be shooting things that don't move, you could always put the camera on a tripod or other support, then you can shoot at just about any shutter speed and get a pretty sharp shot.