Decide on a Certain Budget and Stick to it:
Photo gear has a lot of wana haves, nice to haves and let me have that one as well, gadgets. most camera manufacturers provide a basic memory card of 16 MB, this will be good for only a few high quality pictures, I strongly recommend you will buy a 128 MB or even better yet 256 MB Memory Card. Since Digital Cameras use LCD screen, batery consumption is much higher than what you are use to in film cameras, it is recommended to invest in a battery charger. Allocate a budget for your camera, but make sure it includes the Camera + Memory Card + Battery charger + case and even consider Wide Angel Converter.
How Many Mega Pixels?
The very basic " Point & Shoot " models can start with 2 Mega and can give very good results but I recommend you choose 3 mega or even 4 Mega for prints of up to 5 x 7. If you don't need many enlargements it is high quality and sufficient. There are compact models with even 7 Mega pixels but for all practical reasons it is an over kill, I would invest in wider aperture lens and longer range zoom. Don't think if your neighbor bought a 7 Mega camera that his camera is better, It's not.
Zoom Range:(Optical)
The longer the range the better, you can catch a distant object, make nice close ups and portraits, it gives you more accessibility, flexibility and creative options. A long 420 mm (12 X) is excellent range BUT, you need to understand that the longer the zoom range the bigger the amplification of any hand shaking with the camera, therefore it is recommended to hold your breath, be as stable as you can with your hands and body but even better yet to use a Tripod. I would even compromise a bit on the range to be 370 mm (10 X) " only ". Important feature on a long-range zoom is an Anti-Shake or Image stabilizer. These features compensate approximately one f stop or more on movements.
I referred here to Optical zoom, there is a digital zoom in addition but usually the quality of it is very low, some salesmen tend to confuse the customers by multiplying the optical zoom by the digital zoon and claiming the camera to be 12 optical x 4 digital = (48 X)! Ignore such statements, refer just to Optical zoom.
In the old Film cameras a long zoom range meant a very long bulge, in the current modern Digital Cameras it extends less than an inch and stops, all the rest is done internally by the Cameras optics.
Wide Angel:
Most Digital Cameras do not have wide angel! It is one of the their biggest shortcomings, 36 mm or even worse 37 mm is not a wide angel zoom, as a result when taking pictures indoor you will notice you cannot catch a better part of the scene or only part of the room, when shooting outdoor you will notice that only part of the landscape can be included in the frame. Not to worry, there is a solution! Wide Angel Adaptor, it is an add on which is placed over the existing lens. It can be (X 0.75) = 28 mm, it can be (X 0.66) = 24 mm which is excellent. There is an additional charge for adopters as they are produced either by a third party or the original manufacturer of the camera. Adaptors give small Distortions so as a rule of thumb it is much better to have the original manufacturer adaptor as it matches optically much better. There are even Macro ad on Adaptors available
LCD Screen:
The bigger the better, average size is 1.8", but there are models with 2" and even 2.5", another feature is a swivel (flip-out & twist) LCD screens, you can show your kid His picture in real time, and it can help you take a difficult angel and access shots. The LCD screens have one big problem, that is, under sun light and outdoor conditions it is very difficult to see the picture on them. Therefore, if it has Anti Glare feature it's better. The more pixels the better.
Optics:
The quality of the Glass Optics is Important, some of the Manufacturers wave with their Optics Brands well known producers like:
Leica lens
Carl Zeiss lens
Schneider-Kreuznach Variogon lens
Nikkor Lens
Canon Lens
Etc’.
Additional points:
Auto Focus - The more points the better - (9 Points is very good).
External Flash option via hot shoe a plus.
Lens Protective Hood - Better Light input + physical protection of the lens.
Skin tone:
Test the cameras quality by taking a picture of people, observe the skin tone (face, hands etc'), does the skin tone looks natural to you? Or is it too pale or yellowish? Is it too reddish or pink? Insist on a good natural result.
Who is the Camera manufacturer?
Most of the Digital cameras are designed in Japan, it is very important to choose a reliable producer with strong and experienced knowledge of Cameras, with a large variety of models and commitment to service and excellence. Always think who is the manufacturer, is he coming from the film field, Printers producer, electronics or has he dealt with cameras from day one