Plus and minuses to wood.
Plus -- hardwood adds more to the resale value of your home. Hardwood won't trap dirt and allergens the way carpet will.
Minus -- Initial cost. Hardwood install on stairs is expensive. In my 3 years selling flooring at a major home improvement warehouse, I have
never sold a wood install on stairs. There are a lot of cuts involved and more intricate labor, especially to position the nailer right. Glue down might be easier, but install on stairs is rarely easy. Does that $2600 include the hardwood and other materials? If so, that doesn't sound too out of line.
Carpet, like I said, may trap allergens, but does have advantages. For one, the material and installation is less expensive. Also, carpet will provide more traction and help prevent slips and falls.
If it were me, I'd get carpet with a fairly short pile and a high density that will hold up against traffic. Best way to tell a high density is try to dig your fingers in. You want something where the fibers are nice and close together and you can barely get to or see the backing. I wouldn't recommend a loop berber because you will get smiles at the edge of the stair. A frieze would be good to hold up to traffic but usually aren't high density.
Hope this helps.
