It is far cheaper to buy a drill and bits, predrill the holes and tap the nails in slowly.
If you're just talking about the treads, the rule of thumb is that the nail should penetrate the framing by 1 1/2 times the thickness of the material being fastened to the frame. so, a one inch tread will need a 2 1/2 inch nail or an 8d finish nail. A brad nailer won't drive a nail that long so you're looking at a finishing nailer.
Good luck with your project. I think more people should replace treads rather than try to cover them with other materials.