If we narrow it to just the application or intended use of the knife, then you will look at two main things in the chemistry – carbon and certain alloying. If you want a small knife that will do lots of slicing and little to no chopping and you want it to keep doing that job as long as possible, then you will want more than .8% carbon. Other alloying that will help out will be elements that will turn the iron carbide into fiercer carbides, but you don’t want them to get too out of hand or too large. Look for vanadium, niobium (columbium), tungsten and chrome, but only to a point.
For just simple iron carbide and ease of working, the 10XX steels would be 1084 or 1095. W1 and W2 would be very simple tool steels, but next would come more complicated ones like O-1 or A2.
These are based just upon the type of knife with simple tools, the more involved your tools and equipment get the more steels that you will also have to choose from, and O1 and A2 are kind of pushing it for simple bladesmithing setups. Proper steel selection is one of the most critical aspects of success in making an excellent blade, but the one most often overlooked. Many would be smiths put unnecessary obstacles in their way by choosing steels based on cheap or free supplies, what is most readily available to them, or just using whatever the other guy uses. Furthermore, if steel selection is given due consideration, the aspect of matching skill level and equipment to the appropriate steel to get the most out of it is often unfortunately left out of the equation.
The opposite end of the spectrum would be carbon from .60% to .8%, and things like silicon and nickel to make for tough blades that will see a lot of chopping.