Metal knitting needles are often made of aluminum. They provide a very smooth knit, especially for more complex stitches. These kinds of needles are often favored by more advanced knitters. They can sometimes be slippery, which can be a drawback for beginners or when knitting with a sateen yarn.

Bamboo and wooden needles are very similar. They are usually warm to the touch and very easy to grip. This makes them a good choice for knitting beginners. However, they are usually not as sharp as metal needles, making them undesirable for more intricate stitch patterns. 

Plastic needles are often very affordable, giving people a low stakes way to try knitting without a large financial commitment. They are relatively lightweight, and offer good grip and ease of use. However, they are prone to warping and bending when knitting a tight pattern, and low quality plastic can snag yarn. Plastic needles are also the least sustainable option, considering how often they would need to be replaced. 

Straight needles are the most commonly used type of needle. Preferrable for beginners, they are easy cast on to and even easier to knit with. However, they have their limitations. With straight needles, you can only knit "flat," meaning your project may have to be assembled with a darning needle (a large needle that is typically blunt, used to join knitted pieces together) if there are multiple pieces. 

Circular needles (my favorite) are great because you can knit "in the round" with this style. This means that when you knit your first row, you join your casted on stitches to make a continuously increasing piece. You can also knit flat with these needles, if you want. These needles, like all needles, come in various lengths, but rather than the needle shaft varying, the flexible cord is longer or shorter. Some projects also require you to use different sized needles, providing a smaller or chunkier stitch size. Circular needles are great for this, as many sets are interchangeable, allowing you to twist off the needle shaft for your desired size. 

Double pointed needles are the most complex to use. Most projects don't require you to use them, and circular needles are almost always are great replacement for them. Often abbreviated as DPN, double pointed needles are ideal for knitting socks and i-cords. However, as stated above, you can accomplish both with circular needles. Really, it is a matter of preference.