I want to remove the carpet. cover the stairs with something and finish the risers with wallpaper.
First you need to pull the carpet up and assess what you have to work with. In many instances the stair treads need to be replaced. Then finish the risers with wallpaper. It has the potential to turn out beautifully, you just need to decide if you want stained wood stair treads or painted treads.
I think you my find Grillo Designs DIY blog helpful -
this is her post on her beautiful painted stairs
and this post talks about wallpaper as floor covering which I think would convert nicely to riser on the stairs
If you rip off the carpet, you will have to see if you've got builders grade wood product or wooden treads..... wooden treads are sold by many of the big box home stores like Home Depot and Lowes, if you want a specific wood.... http://www.stair-treads.com/replacement-stairs
If you have old treads I would try Rejuvenate on the wood to make it come back to life.
As to putting wallpaper on the risers, remember this is gonna get kicked a million times, so I would put a few coats of poly over that wallpaper to try and protect it.
Here are some fun wallpapering ideas: https://www.hometalk.com/search/posts?filter=wallpaper%20stairs!