Astrophotography subject matter can be divided broadly in to three categories for the purpose of acquiring a suitable camera. These are scenic photography, lunar, planetary ansd solar work, and deep-sky photography.
The term scenic astrophotography is used to describe work undertaken with a camera mounted on a tripod. Subjects might include the Moon seen through the branches of a tree, the crescent or full Moon, the broad swathe of the Milky Way, and atmospheric phenomenon such as the aurora borealis and aurora australis. Work of this type can be undertaken with consumer compact cameras or DSLRs equipped with short telephoto or wide-angle lenses. Shutter speeds of up to about half a minute can be used with the camera mounted on a tripod and equipped with a remote release to eliminate camera movement at the moment of shutter release.
Lunar, planetary and solar photography encompasses the principal subjects found in our own solar system - the Moon, the planets and their larger moons, and also the Sun itself. These bodies are relativel bright so exposure is not generally a problem, but high resolution is important to capture surface detail. Good photography of this type can be undertaken using webcams to capture large numbers of frames that are then combined with specialized software to extract the maximum amount of detail.
Deep-sky subjects include everything not incorporated in the previous two categories. Interesting subjects include galaxies, nebulae and star clusters. Objects such as these are very distant and hence much less bright, so long exposures, more sophisticated or specialized low-noise cameras and long-exposures are required. Low-noise DSLRs can be used for this type of work, although dedicated, cooled astronomical CCD cameras are the best option.