DON'T buy a camera just because it has HIGH MEGA-PIXELS... Factor in everything. Just remember, a camera that takes a 5 mega pixel image does not take a better quality image than a 2 mega pixel camera. It simply means, the 5 mega pixel camera can take an image that is larger, but it is still the same quality (in other words, the dpi (dots per inch) is the same, but the size of the picture is larger). This is a very important point that most consumers don't realize.. 3-5 Mega Pixels is generally a good option, preferring the 5 Mega Pixel end.
An Image Stabilizer option on your camera is VERY IMPORTANT...(a lot of the better camera's come standard with this now) which basically means you can take pictures even if you have the shakes, and it comes out very clear, it also lets you take movies in stable mode, whereby you can get crisp pictures and movies without having to use a tripod and the clarity is perfect, eradicating blur and fuzziness from not holding the camera super still.
DIGITAL ZOOM is a waste of time....Digital zoom simply enhances the photo digitally, so it just makes the pixels larger as you zoom in, whereas OPTICAL zoom is true zoom, in other words, it zooms in with NO loss in quality because it literally uses the LENS option to zoom, it becomes very evident when you try to zoom in on a picture and as soon as the digital zoom takes over, it gets very choppy and blurry. Try to get something starting at 5 x optical zoom, it doesn't matter what the digital zoom number is, you'll see what I mean, it is kind of pointless using digital zoom.
MAKE SURE YOU GET AN AV CABLE AND THAT THE CAMERA HAS THE OPTION TO PLUG ONE IN....This lets you connect your camera to a television, it is just sooo much better showing the family your movies and photos on a tv, rather than huddling around your computer, or worse, trying to watch some tiny little screen on the camera, and besides, everyone has a TV that you can use to show people your photography. It becomes a lot of fun aswell, showing your xmas movies/birthdays/holidays/celebrations all on the TV to the whole family. Just change your TV to the AV setting, and plug the camera in, and away you go, instant family viewing, everyone will love it.
The viewfinder is important, make sure you get one that starts at 2 inches, otherwise its kind of hard to review your pictures on them. And if you can, a flip out viewfinder is just soooo handy, so that you can move it into any position without compromising taking the picture.
MAKE SURE you purchase a fast battery charger that can charge your batteries in about an hour or so, and try to buy a camera that takes standard AA or AAA rechargable batteries, otherwise if you purchase something with a special battery, you will have to bring the charger with you everywhere you go and try to find a charger socket which sometimes can be very inconvenient. And AA or AAA batteries are always available from anywhere. If you don't use rechargable batteries its going to cost you a LOT of money in batteries if you don't, and make sure you purchase the NiMH type batteries which are the most powerful (some cameras wont even turn on unless they are NiMH)
On purchasing a Memory Card, you will need a LARGE one, preferably a gigabyte or 500MB card. You see, to take movies with a digital camera, it usually takes movies in 640x360 mode, or 320x180 mode which after 8/16 minutes of recording (depending on which mode), can fill the card. Its also a good idea not to purchase additional Memory cards, on the basis that you should just purchase a multi-media storage device instead, so you can take both with you on a holiday, and once the card becomes full, you just transfer the contents onto the device, and then you can start taking photos/movies again.
MAKE SURE YOU GET A FAST SPEED MEMORY CARD...otherwise if you don't, you will be wasting your money, and if you are recording a movie at 640/480 resolution, with 30 frames a second, your card wont be able to keep up with the amount of data being recorded, and will crash after 1 minute or so. A good standard card would be 120 x speed, or in other words, something that writes at 9 Megabytes a second.
Movies: As far as movie "quality" goes, try to get one that has 30 frames a second AT LEAST, otherwise your movies will look like old fashioned choppy movies from the 40's. FPS means Frames Per Second. Be careful not to get confused between the frames per second and the quality. If a sample movie you are watching is recorded in 60 fps -which is a new feature on many cameras- and you try to compare this to a movie recorded in 30 fps mode, they are going to look very different. Obviously the 60fps movie will look realistic and clear. So make sure you are comparing movies with the same frame rate. Essentially the more frames per second the recording is, the less blur you will notice, and you may be confusing this with "low quality imaging" by mistake.
Make sure the shop that you intend to buy the camera from will accept a refund after 2 weeks or so, because like with myself, after taking the camera home, you may not be entirely satisfied with its performance, and may want to purchase a different camera, and its better to have that option up your sleeve.
Protect your LENS!!!! Don't let anything touch or hit the lense, and always protect it, it is the engine of your car, and is vulnerable, so take heed.
Make sure you try the camera in the store or ask for samples of it INDOORS, not OUTDOORS, all digital camera footage looks good outdoors, but a true test will be recording movies indoors, and taking still shots indoors, TRUST ME!
If you are going to purchase a digital camera for the movie option aswell, which most people do, TRY to get one with Stereo sound, and at LEAST Mono, otherwise its kind of silly recording movies without sound. But stereo sound is about 500 times better than normal Mono (single) sound recording cameras.
And when all other advice fails, try to purchase a well known camera for its name: Canon and Olympus are probably two of the most trusted I can recommend. If you have the option for an extended warranty, take it.
I hope this helps, and have fun with whatever camera you purchase.