JPEG is a compact file format where an image is compressed digitally using a software algorithm and was used prior to digital cameras to save space when transmitting images over telephone lines. This was great for early digital cameras and PCs which had limited memory facilities, however today space is not such a critical factor with SD cards offering 16|Gb and 32Gb as standard and hard disk drives offering 1 terrabyte of storage. However it has become an industry standard and all digital cameras can shoot JPEG.
RAW format is a format which captures the image in your camera uncompressed or with minimum compression, so there is more detail in the image which can be processed later. However RAW is not a standard. Nikon call their RAW images NEF, while Canon call theirs CRW.
Imagine a line of 64 pixels within an image. You could describe the line by saying something like "red, red, red, green, green, red, etc" This is the equivalent of RAW. However, you could also describe it as the formula "14 red, 3 green, 16 red, 6 green, 24 red, 1 green" this is the equivalent of JPEG compression.
It is obvious that there is more detail in a RAW image which can be manipulated in post-processing, but a RAW image takes up more space than a JPEG image. This is a major advantage for photographers who may want to bring out some detail hidden in the shadow area of an image. With more data to play with and shooting a large image size such as FX, professional photographers can make very large prints of their photos without any significant loss of image quality. For amateur photographers who only make small prints or who only publish to websites where image quality is small, JPEG is probably sufficient.
The choice is yours. If you do a lot of image manipulation it is probably better to shoot and manipulate RAW images. If you just shoot for fun and don't edit photos much then JPEG is probably sufficient.