Types of Cameras
Point and Shoot (P&S) - This is the type of camera that is often very thin. P&S cameras generally don't have options on them for controlling shutter speed, aperture, ISO, etc. They are fully automatic, and usually have a large LCD screen on the back (digital) for taking a picture.
Advanced P&S - This is the kind of camera you will want to start with. They are small, but resemble DSLRs, they may have a flip up flash, handle, etc. But the main reason we want them, is they they take better quality pictures, and you can control the aperture, shutter speed, and ISO (among other things). The reason they are good to start with, is that they can be fully automatic, but you have room to grow as you get better,
SLRs - SLR stands for Single Lens Reflex, if there is a "D" in front of it, than it means a Digital Single Lens Reflex. SLRs are the cameras that professionals use, they are the ones that have interchangeable lenses. There is no LCD screen for viewing the picture before you take it, rather, you use the view finder. The way it works, is that light goes in through the lens, reflects against a few mirrors, and through a prism, so you can see it through the view finder. When you click the shutter button, the first mirror lifts up, and the CCD image sensor, or frame of film is exposed to the light. Picking the one for you
*Note* Megapixels are not the way to chose a camera. More megapixels does NOT mean a better picture. A larger image sensor does, but while you are at P&S cameras, they are all generally the same. This is more important when you choose a DSLR.
This is based on you getting a Digital Advanced P&S:
Until you get to SLRs, there isn't a lot you need to worry about when purchasing a camera. First, look at the features. The wider the range of shutter speeds available, the better, along with the range of apertures. Look at how much zoom your camera has as well, if you tend to zoom in a lot, go for one with more zoom. Check out what kind of memory card the camera takes, and how much the cards cost. Ideally, you will get a 1gb card. If the camera takes SD cards, you may want more, in case you ever upgrade to a DSLR that uses SD. Lastly, look at aesthetics, and how comfortable you are holding it.
If you are getting a DSLR, I will mention something about the brands to get. I only recommend Nikon and Canon, and to explain this bias to people, I've invented The iPod Analogy. If you look at mp3 players, you'll notice that the iPod is not the most economic player. Other brands provide cameras that may have more features for your money. The catch is that the iPod is compatible everywhere, any feature associated with music is built to work with an iPod, and not as much other brands. Cameras are the same way, you're much more likely to find the lenses and accessories you want if you have a Nikon or a Canon.Where to buy
Two very common places to buy cameras are:Best BuyBH Photo Video
BH often carries their equipment for much lower prices. Make sure to get a warranty for your camera.