The first issue you have to face is will anything stick to the existing finish? Some of the more modern finishes not have anything adhere on them.

"Sanding the old finish off" is rarely a good idea. You will regret it soon as you gum up piece after piece of sandpaper. Not will it completely remove the existing stain and finish in all cases. A stripper is the way to go. You really need to have bare wood to get a good job with stain.

For the areas you are painting, assuming it's a finish that will accept a top coat, you will need to clean and scuff sand it. I am partial to BIN primer, a pigmented shellac. Shellac bonds to most everything and everything bonds to it. As far as "filling the pores," that really depends upon how much of the pores remain after sanding and priming.

Hey Bobsmyuncle I was hoping you'd come to the rescue. You gave me lots of info. to refinish a desk awhile back. I failed to complete it because I'm too chicken to use a harsh stripper. The top was the only part I got done. I'd love to take a hands on refinishing class but there's nothing like that around here.

Anyhow, If I use a stripper to remove the existing finish do I need to take down the stairs? (I'm hoping you say no.) What about ventilation? Can I just open some windows and use fans?

As for painting, I know my Dad took all of the stair pieces to his work and sprayed a clear coat. I don't know what it was but could find out. Just clean and 'scuff' not completely strip the protective clear coat?

Thanks for the BIN suggestions. I'll use that if I ever get brave enough to try this. With the BIN after you sand, prime, is there a chance you would need to lightly sand and prime again or should one coat do it? I'm assuming there are directions on the stuff but was curious.