Firstly, you have to think about one of the most important factors of a camera. Quality!
To me, quality means, a clear and crisp picture, the ability to adjust settings to give you the perfect picture for a perfect enviroment, and its worth the money!
So with this in mind, you then need to think about what camera would 'suit you'. If your fond of taking pictures of landscapes and scenary, then you need a camera that has advanced white balance and light settings, and possibly the option of an additonal wide angle lens. If you just want something quick and easy to take pictures of most things, especially parties- Then you need something with a built in flash, and something that looks easy to use.
If you want to 'go pro' then you'll start entering into the Digital SLR zone, where rivals such as; Canon, Nikon, Sony and Olympus, All produce some outstanding cameras! There is no real advice to give on choosing the right SLR, as there are so many out there. My best advice is to compare. Make sure you read at least 3 reviews on your desired camera, and then match it up against another camera with a simlilar price tag. A good example of this is the Canon 550D and 600D. The 600D is the upgrade to a 550D, but it's not necessarilly the better camera.
Overall, make sure you buy the camera that feels right, and doesn't blow a gigantic whole in your wallet!