There are many different sizes and styles of nosecones, each suited for different applications

Mach Considerations

Before choosing a nosecone design, one important thing to think about is the maximum speed of your rocket. Once the rocket hits the mach transition zone (generally around Mach 0.7), the air traveling over the leading edge (tip) of the nosecone will begin to heat the rocket considerably. To counteract this, a metal tip is usually installed on any rocket that will fly above Mach 0.7. The exact length of the tip is usually not important, but usually, 3-4 inches is chosen, as it gives enough space to manufacture and retain the nosecone tip easily. 

A metal nosecone tip also helps with flight stability, adding a large amount of weight as far up the rocket as possible will move the CG upwards and increase stability. 

Nosecone Shoulder

Most nosecones slot into the tube below them with a pre-installed coupler. While this is considered part of the nosecone, it is not counted in any discussions regarding the shape or length of the nosecone itself (since it is inside the airframe).

Nosecone Ratio

The ratio of a nosecone describes its length (measured vertically from the tip to the start of the airframe) as compared to its diameter, i.e. a 6" airframe rocket with a 5:1 nosecone would have a nosecone that is 30" from base to tip. At certain speeds with certain geometries, some nosecone rations work better than others. 

Nosecone Shapes

There are multiple shapes of nosecone, each one optimized for a different airspeed. Below Mach transition, the shape of the nosecone is not very important, and whatever reduces weight is best. 

Above Mach 0.8, the chart below from the USAF DATCOM can be used to identify the ideal nosecone shape, using the following scale:

Superior - 1, Good - 2, Fair - 3, Inferior - 4.

It is important to note that this chart does not cover tangent ogive nosecones, the most common shape used in modern rocketry, which generally performs about as a 2 or 3 for all mach speeds represented in this graph.