Before narrowing down your choice of a particular make and model, here are a few things to consider when looking for a compact, point & shoot digital camera that is best for your needs:
1). Requires AA batteries or not? There are many cameras that all you do is recharge, (like a cellphone), the camera. I like cameras that use AA batteries. You can buy rechargeable AA batteries for your main source of power, and buy non-recharge ones in a pinch anywhere, should you find your camera without power, instead of being without a camera to use while it's hooked up being recharged. (What happens if you need to replace the lithium ion battery? Might be costly to replace and not convenient to find). It's true that digicameras use up non-recharge batteries quickly. But you can buy rechargeable ones and they last a long time. It should be a must to buy rechargeable batteries (with it’s charger). There are some rechargeable AA (stick with the name brands), that now recharges in an hour, or even less! (Remember to figure in the cost to buy rechargeable AA battery and battery recharger).
2). Media Memory Format? SD (Secure Data either MMC [media memory card] or HC [High Capacity]) I know for sure this 'memory card' is used by Canon, Kodak digicams; and I'm sure they're other brands. Then there are other brands who require xD and CF (Compact Flash) and Sony uses exclusively their memory 'sticks' (pro Duo and other different configurations). The pros for having a camera that uses SD card, is that they are also used in other electronic devices and are the most affordable media memory storage.
3). An optical viewfinder is very useful for those times when it's difficult to see your subject on your screen, i.e. a distant face in a crowd; too sunny to see subjects in the LCD screen; fast action shots. It can help conserve power of your camera by periodically turning off the LCD screen and using the optical viewfinder. This feature seems to be important to some, (me included), but to others, not necessary. (This is where IS [Image Stabilization] comes in. Helpful if your camera does not have an optical vierfinder.)
4). Don't get sucked in by the more MP (megapixels [10 and above]), the camera has, the better. It is not always the case. 5-6 mp is sufficient for most.
5). Optical zoom of at least 3-4x. Higher optical zoom, a bonus. Don't be fooled by a high digital zoom number. Opitical is what you're looking for.
6). IS (image stabilization) and face detection? This is a personal choice for what an individual wants, and on some models, it's a standard feature.
7). Camera size: Compact or subcompact? You might compromise in some functions and options when you go with a small and sleek camera. Camera size will dictate what functions and features will go into the camera. This too, is a personal choice for an individual.
Don't forget to consider in your budget: Rechargeable batteries and extra memory cards/sticks. Good to have if your camera also takes video. Nothing more frustrating than running out for memory space on your card/stick.
In no particular order, here are some of the best and popular brands: stick with Canon, Nikon, Sony, Olympus, Fuji, Kodak, Pentax. They have models that can fit any budget.
These are the basics when researching and shopping for a digicam. Don't worry about other features, they all have pre-set settings for a given photo situation, and some fun ones too. Most, if not all, also take video. (For good quality shooting video, set at 640x480 at 30fps.)
If you do your research on cameras, then go to your local electronic/camera merchants like Best Buy, RadioShack, Circuit City, Ritz, etc...or even Target, Wal-Mart, Kmart, Costco, Sam's Club, or consider your office supply stores that have a camera dept., OfficeMax, Staples, Office Depot. Or check on-line. A good place is B&H.