This is a common question from those who are at the early stage of building out their kitchen (a less common question for those who have 100+ knives in their shed).
Fortunately - for those asked this question who have experience as a chef or cook the response is almost as common as the questions.
The First Knife - The Chefs Knife or Gyuto Knife
If we are trimmed to only 1 knife (let alone 3) just about any chef will request the chefs knife or referred to as the Gyuto knife in the Japanese collection. The chefs knife is the all purpose blade that is made to be able to cut anything. Dependent on the arm length or the holder we are usually looking at a blade starting at around 18cm and going as far as 24cm (if the holder is 6ft 6...an NBA basketballer for example).
The handle should be balanced in weight, for the chefs knife this will be a bit more than a Gyuto knife as the blade itself typically weighs more in the western world. Most knives have a heel and belly which allows the holder to chop down on tough ingredients like pumpkin or watermelon with a finer blade as the tip is approached. This means you can do both heavy duty and intricate work with the single blade.
That said, making it all purpose means it is not typically the best at anything - a meat cleaver or Bunka Knife is a superior heavy weight chopper, for vegetable cutting the Nakiri Knife would be the best performer and for intricate work most would go with a paring or utility knife. That said - the Chefs knife or Gyuto does everything "ok" so it is the worlds most popular knife and the most important knife in a three knife collection.
THE CHEFS KNIFE
The Second Knife - The Utility Knife
Sometimes we need to be intricate and we can use either the paring knife or the utility knife. With both of these blades our hands are closer to whatever we are cutting allowing details to be displayed with either of these blades. The wonder of the utility knife is that it is big enough to chop most things as well - where there paring knife is not.
Much like the Gyuto knife or chefs knife it is a knife that does everything. For those with a smaller hand or a focus on intricate cutting (like herbs or the kids lunch) the Utility knife is potentially the most important knife we hold - hence it's inclusion in one of the three most important knives you can invest in.
The Third Knife - The Serrated Knife
The third knife is a serrated edge cutter - which allows you to slice bread and tomatoes even if you forgot to sharpen any of your blades for months at a time (we are not promoting not sharpening but we understand it does happen). Usually we are looking at a middle to longer length serrated blade edge so it cuts loaves of bread at any size and scale and has a blade which is long enough to glide through a crusty baguette or unconsciously soft panini - it works on all breads.
One other thing to note on a serrated edge is that is usually sharpened on only one side - scallop or serrations are extremely hard to sharpen (due to the serration itself) so when you peer at the knife and see it only has a bevel at the tip of one side this is normal.
So that's it. If you only have three knives to take you from breakfast to dinner for the next ten years - the chefs knife, the utility knife and the serrated edge knife should be your collection.
BUT - if you're anything like us and most of the knife wielding community - these three knives are just the beginning.
*Thanks to Sven Knives for allowing us to use their sketches :)
In addition to the notes above you can watch video below where numerous chefs echo a similar point of view....