Things to look for:
Megapixels:
If you only ever want to see your pictures on-screen or make small (6"x4") prints then 2 or maybe 3mp is fine.
If you will ewant to make larger prints, say 10"x8" or something like that, than you'll need more like 4 or 5mp.
Note that, all other things being equal, the image quality from a 4mp sensor will almost certainly be a little better than a 5mp sensor (it's to do with signal-to-noise ratio in the individial photo-sites... more pixels = smaller photosites = lower SNR).
In practical terms, the differences may be small, but you should be aware that "more is better" is not necessarily the truth.
Lens:
If you're looking for a zoom lens, pay attention to optical zoom only. Digital zoom is a con - all it does is magnify the central portion of the image. It is simply chopping off the edges of the picture, so if you have a 4mp camera and use 2x digital zoom you end up with a 1mp image from the middle of the sensor. You lose quality and cannot enlarge the resulting image without being able to see the individual pixels.
Beyond that, the rest is pretty much up to you. If you want lots of user-selectable settings or a simple point and shoot, that's just a case of choosing the camera with the features you want.
Many pocket-size digital cameras have oodles of 'real photographer' options, but they can be of limited use (I've got one, and use it almost exclusively on Auto because the amount of creative control - controlling say, depth of field - you really have is very limited thanks to the laws of physics)
Forget talk of brands - no brand is intrinsically better than another in the middle ground. There are some poor makes at the very cheap end, but once you're in the mainstream there is no 'brand' difference between Canon, Minolta, Pentax, Olympus, Samsung, Panasonic, Sony, Konica etc... They do have differences, but they tend to be in style, control layout etc. So choose what looks and feels right for you.
There are some good sites for information - http://www.dpreview.com and http://www.steves-digicams.com are two of the best. You should be aware that these guys exist to make minute differentiation between cameras. If the say one camera is a dog then it is. If they say camera a is a little better than camera b, then the difference will be too small to notice in real life. Look at the broad results of the reviews and not the minute detail.
I hope that helps? :-}
Cheers,
Dave.
