One thing you should keep in mind is that the stair carpet is walked upon heavily and often, so a durable carpet is essential. You should also make sure that the carpet is not too thick, as a thick carpet will not fasten into place well.
As the stairs are such a high traffic area in your home, you should make sure that you buy the highest quality carpet and carpet pad that you can afford. This is also due to the fact that footfall on your stair carpet will be heavier due to the force of gravity. However, stairs are not usually prone to stains in the way that other rooms are, meaning that you can consider a light carpet with an attractive stair runner.