Choosing the right type of knife
Choosing the right type of knife for your particular circumstances can be tricky given the vast amount of options available. The following chart can help you narrow the field of possibilities. You can click on the image to see it full size.

Choosing the right steel
Once you have chosen the type of knife you want, one important question remains. What steel should you choose? Once again, this depends on your context and your purpose. Two important factors to consider are 1) the amount of time you are willing to spend caring for your knife, and 2) the amount of money you want to spend.
Carbon steel blades require more care. They need to be cleaned and dried quickly after use or they will rust. However, when maintained properly, they develop a beautiful patina that acts as a testament to all the delicious dishes you have prepared. They are also a bit easier to sharpen.
On the other hand, if you don’t want to have much maintenance to do, a stainless steel blade is the way to go as it will not rust even if you leave it wet sitting next to the sink.
Finally, if you have a larger budget, you can consider powder metallurgy steels. These high-end materials offer uncomparable performance, granting you a very long lasting edge.