Which should you shoot: RAW or JPEG
Simply put, JPEG or JPG makes the most sense for most people. JPEG files by definition compress image information.  This allows them to be smaller than non compressed image formats like RAW camera files or TIFF editing files.  JPEG images look great to the eye and require much less memory space on memory cards or computer hard drives. Small file size also means that image recording time in the camera is short, allowing faster shooting of multiple images. JPEGs are usable right out of the camera. No further processing is required to obtain a usable image. The ease of use makes them ideal for sharing pictures quickly and broadly. That is one reason why JPEGs have become the primary internet image standard.

What is JPEG?
JPEG or JPG (pronounced "jay-peg") is a standardized image compression mechanism for either full-color or gray-scale images of natural, real-world scenes. JPEG is an acronym for Joint Photographic Experts Group, the original name of the committee that wrote the technical standard. JPEG is designed to exploit known limitations of the human eye, notably the fact that small color changes are perceived less accurately than small changes in brightness. Thus, JPEG is intended for compressing images that will be looked at by humans. If you plan to machine-analyze your images, the small errors introduced by JPEG may be a problem for you, even if they are invisible to the eye.

JPEG images also record only 8 bit per color channel.  This means that each pixel has 8 Red, 8 Green and 8 Blue bits associated with it to carry color image information.  As a comparison, RAW images ( which are covered in more detail below) offer 12 bit color depth, i.e., 12 bits for each of the three RGB colors.

JPEG is "lossy," meaning that the decompressed image looses image quality from the one you started with. (There are lossless image compression algorithms, but JPEG achieves much greater compression than is possible with lossless methods.) JPEG file compression can be varied by adjusting image parameters. This allows the image maker to trade off file size against output image quality. You can make *extremely* small files if you don't mind poor quality. On the other hand, if you aren't happy with the output quality at the default compression setting, you can improve quality until you are satisfied, and accept less compression.

JPEG images have become the primary international standard for transmitting pictures over networks because of small file size and controllable display properties.

This link will take you to the official JPEG, Joint Photographic Experts Group , WEB site, Click Here.

What is RAW?
As the word implies, these are the ‘Raw’ image data from the imaging sensor in the camera. To use a RAW file, software processing is required. After processing, a standard image file is created, usually a TIFF file which offers full image quality and information for further editing without loss of image quality. RAW files require much more memory storage space than JPEGs. Another aspect of large file size is that the original image requires more camera recording time, slowing multiple image shooting to wait for the recording process to complete.

RAW images offer 12 bits of color information for each RGB channel.  This means that 12 bit of information in the Red, Green and Blue color channel plus 12 bits grey have 48 bits of information associated with each pixel.  The color fidelity of a RAW image is theoretically very high with 16.7 million color scale available to provide a wider range of tones and superior detail in bright highlights and deep shadows when compared with JPEG files. RAW files must be "processed" before they can be opened in your computer's image-editing software. This conversion process typically takes only a few seconds using the dedicated driver software, which will convert the RAW file into a standard 8-bit per channel JPEG or TIFF file, or for maximum tonal range, a 16-bit TIFF.

Generally, shooting RAW is not necessary for making very pleasing pictures. The extra memory space and required processing to use RAW originals makes them the province of only demanding applications.

Shooting RAW vs. JPEG may be a very personal decision. I use RAW for quality critical images, actually for everything.  You, however may find JPEGs most useful for event type shots which are usually taken in large numbers and will seldom be enlarged very much.

More on the RAW VS JPEG Subject
If you would like more technical information about RAW and JPEG images, file processing and the like, I recommend David Eppstein's experiment and discussion.  He offers what I believe are very practical points and objective observations in his information without the hyperbole of some others you may come across.  Along with the description of his work David also includes some large online images for visual comparison that actually show what he describes.  David does not seem to have an ax to grind.