Compact cameras cost slighly less, don't require additional lenses, are lightweight, and picture quality can be quite good.

While reflex cameras (dSLR) are slightly dearer - although prices are now very accessible - and heavier, picture quality is even better. Choose a reflex if you are serious about photography (not necessarily a professional but even a serious hobbyist) or if you plan to sell your pictures at microstock agencies such as Shutterstock and Fotolia (see full list of agencies);

This is a list of what to look for in a camera:

Optics. Even in digital cameras, lenses are still a very important part of your camera. There's no use in buying a 10 Megapixel camera if lenses are small and low quality.

Resolution. Most cameras nowadays are 8+ Megapixel. This is pretty enough if you need to print your photos in usual 6" x 4" (15 x 10) or even in sizes up to A3. Higher resolutions (10+ Megapixels) are better if you plan to sell your photos

Memory card. If you plan to shoot a lot of pictures, you'd better buy a larger card than those usually shipped with your camera. Choose a 4GB+ card.

Olympus, Nikon and Canon are all great and affordable brands both for hobbyists and professionals.

Now many computer manufacturers are building cameras as well. But brands that have a tradition in photography are usually better as far as lenses are concerned.