Your basic options for stairs are wood and carpet. But not only can you use one or the other, you can also use them both.
With wood you have the most options for different looks. Various types of wood can provide different color and grains. You can mix woods with steps of one type while the framework is another. Steps can have different shapes along the edge, be snug with the frame, or extend slightly. There are many style options.
Carpet is a bit less flashy than wood in that you only have the hundreds of different types of carpet available to select from. But there will be less detail in the appearance of the stairs.
You can combine the two options have a wood staircase with a carpet runner along the middle portion. This is an excellent idea to prevent slips and wear to the wood.