It depends on the overall theme of your house and if there are any special requirements for either marble or wood. Wood is softer to tread on than Marble and Marble is easier to clean.

I have some suggestions if you are thinking budget friendly changes. Make a photo gallery with different size frames and arrange them parallel to the stairs, so you can enjoy each photo as you climb up. And for the area that will be on a level with your upper floor, try some pretty decal that will connect the photo gallery to upper level. And last, if you have budget add some beautiful hanging lights in the stairwell. Also think about repositioning your refrigerator.

you can go for wooden style steps available in full step size. different companies manufacture such tiles with various range of colours and texture as suitable to you.

if required a wooden pergola can be added attached to the staircase mumty on left side but it should not exceed from the height of mumty. It will complete the elevation. Also if you love planters then put some creepers and hanging lights over the wooden pergola.