This has been debated on many places in camera clubs and on the internet. Here is my view on the subject.

RAW files are not image files. They are data directly from the camera sensor. They need to be processed after the fact.

JPG files are processed using settings that have been set in the camera beforehand. They are then compressed and stored to the memory card.

I shoot all my pictures in the RAW+Largest JPG mode. Memory cards are so cheap now a days and cameras have big buffers so I see no need to pick one over the other. I really like the RAW files for their flexible ability, but sometimes I use the JPG when the settings were perfect and I'm just looking to do something fast.

When converting RAW files there is a choice of bit depth to make.

8 bit files have 255 shades of each Red, Green, and Blue.
16 bit files have 65,536 shades of each Red, Green, and Blue.

Most digital camera RAW files is a 12 bit file so if you use 8 bit you will lose some color information. If you use 16 bit you have more then you need. Depending on what your taking pictures of you may or may not notice the difference between the two.

I tend to use 16 bit files when I'm doing print work that I deem important. If I'm just processing images for the web I use 8 bit, because you can't use 16 bit images on the web anyways.

When you use 16 but images you are really limited in the file formats you can save the image in.

Color space defines what color is. It defines what color red is. There are three main color spaces for photography sRGB, Adobe RGB, and ProPhoto RGB.

sRGB is the smallest, but most commonly used color spaces. This is the color space you must use on the web since web browsers assume that is what the image is in.

AdobeRGB has a greater range of colors. Many people use this color space when they are working with photos in Photoshop.

ProPhoto RGB is the biggest space of the three. Most people think this is overkill since very few printers or monitors can print the colors that are exclusive to this space.

There are many different file formats that you can save your photos in. I'm going to talk about a few of them below.

PSD files is Photoshop's native file format. It supports everything Photoshop does.

JPG files is the most popular format. It is the most universally accepted format. It is compressed so when you save as a JPG don't open and resave the file. The file will get drastically worse each time you do that. Use this format once you are done editing the file. It doesn't support things like layers and channels.

TIF files is a standard image format that is half way between JPG and PSD. There is many different kinds of compression in TIF files. They can either be lossless or lossy compression.