The first consideration is how many megapixels to go for, and that depends on the use you will have for the camera. 1 mp is enough for e-mail pictures, 3 is supposed to give a sharp enough image to print at A4 size without looking unduly fuzzy. You only need more than 3 megapixels if you intend to print in larger sizes than that. Then consider zoom capability. Optical zoom is "true" zoom: digital zoom is just magnifying part of the digital image (each separate pixel).
After that I suggest you look at the other features of various cameras. Some are "point and shoot" with a few things you can tweak, while others are more like professional SLRs which need intelligent setting. I have had an Olympus mju-300 for nearly a year now and am very satisfied with it. 3 megapixels, essentially point and shoot, 3x optical zoom (and some digital zoom which I never use), small and easily pocketable. Buy a magazine and then go and look at some in a shop. Then look on the Net for a good price!