This is a very common question. There is no one definitive answer but the following will give you some guidelines. There are three essential categories of knives and then a fourth category that we call "specialty knives".
The most important knife to have. This is the knife that you should use for up to 90% of all your cutting needs. Traditionally, this knife is referred to as the chef knife. I think it is better referred to as the cutting board knife. It is the knife used for the majority of cutting on the cutting board. Chopping, mincing, most slicing... Meats, fruits, vegetables. In US and European culinary schools, you are trained to use either an eight- or ten- inch chef knife. Unfortunately, not everyone goes to culinary school and, more often than not, home cooks are talked into buying a long chef but not taught how to use it. So, it sits in their butcher block and is never used. This knife should have a blade wide enough to create a space wide enough so that your knuckles don't hit the cutting board while mincing. For those who are very serious about cooking, a seven to ten inch chef or santoku is optimal. For those who like to cook but are intimidated by a large knife, a wide blade knife as small as four inches can still be quite functional.
Here are several New West Knives that work well for this purpose.
This is the knife that is used when you are holding the food in your hand and cutting it. (Not on the cutting board). Peeling, coring, trimming, decorating... Some like to have a variety of sizes of this knife for different cutting techniques.
Breads are very difficult to slice with a traditional straight edged knife. (Though very sharp, long chef can work). Serrated edges work exceptionally well on soft foods that tend to smash like bread. Serration also is often the best choice for slicing roasts and other large meats.
Though many knives will work for slicing cheese some shapes are much better suited than others. It should be long enough to cut a nice sized piece and have a wide enough blade to pick up the cheese after it is sliced. Some companies produce a knife that has metal removed from the middle of the blade for soft cheeses, but we prefer a solid knife that can be used on all hardness of cheese without fear of bending it.
Tomatoes are difficult to cut without smashing. The can be a real challenge for many knives. We are pleased that all of our knives do an outstanding job slicing through even the softest tomato. But, there are certain knives we will strongly recommend to you. First, you should use a very sharp, cutting board knife or a knife with serration. Serration will easily cut tomatoes without the need for regular sharpening.