Where ever you are on planet earth, 3 knives is the number of your first collection, however depending on where you are these knives are very different.
The First Knife of Your 3 Knife Collection
For those in the western world the first knife you ever need is the chefs knife or chefs kitchen knife. The chefs knife is the ultimate kitchen knife that is built to do just about all - chopping and slicing protein, fruits and vegetables. If you're in the west this is where we begin.
For those based in Japan the first knife is the Deba Knife. Unlike the chefs knife the Deba knife was first built for the preparation of fish, as at that time was the only protein eaten in Japan. It remains the pioneer of the Japanese 3 knife collection however it is now used for other proteins and Japanese kitchens have started to add Chef style knives to their collections (Santuko and Gyuto for example).
The Second Knife of your 3 Knife Collection
The second kitchen knife we use in the western kitchen is the paring or petty knife. This knife is not for protein, it is made for intricate cutting, peeling and even slicing fruits and vegetables with them held in your hand. The chef's knife is a little big (needs to be to chop a pumpkin) if you're trying to peel an apple or remove the greenery of a strawberry - that's why the paring on petty knife is needed.
In Japan there second task is fruit and vegetable cutting and the knife used is either the Nakiri (most common now) or the Usuba. Knife. Once a fish is prepared with the Deba knife, the fish needs to be complimented with pickles and vegetables and the ultimate tool for this is the Nakiri knife. It translates directly - "Na" means vegetable and "Kiri" means slicer.
The Third Knife of your 3 Knife Collection
Once the dish is prepared the is one more knife is needed.
In the west we then require bread and we need an instrument to cut it. Enter the Bread or serrated knife. This knife is long and has serrations along the blade - the ultimate tool to change a loaf of sourdough into slices of bread ready to go.
In Japan they utilize the Yanagiba (or Sujihiki with a single bevel), an elongated slicer to slice fish, vegetables or just about anything (even bread) with a single movement. The Yanagiba caps a two part process of fish preparation and is the ultimate knife for final presentation.
So the Western and Japanese 3 Knife collections are quite different.
In Australia, the three knife collections is the chefs, paring/petty and serrated knives. In Japan they start their Japanese 3 knife collection with a fish/all-purpose chopper (the Deba), a vegetable chopper (The Nakiri) and a slicer (the Sujihiki).