Remember that cameras don’t come cheap so think long term and buy a good quality cam from a reputed company only [eg. kodak, sony, philips, panasonic, sanyo, JVL etc.]. Insist on having a camera with at least 1 year warranty/guarantee. Don’t go in for cheap China made ones. They get spoilt easily.
Decide how many megapixels you want your camera to be. Megapixels is a measure of how many patches of colour make up your screen. Higher the number, better is the picture quality and detail. But too much of detail is not good as it may highlight features that you may want to hide [eg. wrinkles]. So think about it. A 3-5 megapixel camera is quite good. There are cameras available that offera variable megapixel range. These are a bit expensive but a good long time investment.
Size matters. Decide how big you wnat your camera to be. A large camera may be difficult to carry around. A small camera comes without a lot of useful features. Generally a medium sized camera suits most people and is also affordable. But the final choice depends on your requirement.
Make sure that your camera has video capture if you want to shoot movies with it. most cameras these days come with still as well as movie capture features so buy them.
Go for a zoom that fits you. A 3x zoom zooms upto 3 times withoug blurring the picture while 10x can do it 10 times. However, generally a 3x zoom suffices for most people and is not very expensive.
Consider what special scene modes you might use before you buy. Digital cameras often come with scene modes that allow you to take pictures in various settings, such as the beach, indoors or sporting events, using automatic settings tailored to the scene. Take a look at the viewfinder of the digital camera. Viewfinders vary in size, so think about how big of one you want. Some also swing out from the camera allowing you to hold them at different angles. This is an important feature if you like to experiment with different photography angles. See if cameras you’re considering have image stabilization technology. Image stabilization technology helps you take sharp pictures of moving objects. This is an important feature if you plan to take a lot of sports pictures. Give some thought to what type of batteries you want the digital camera to use. Some take standard AA batteries. Others take special lithium batter packs. These are more expensive to buy, but last longer
I hope this helped