I actually just had this done. I knew I wasn't talented enough to pull it off myself, so I paid a professional painter to do the project. I had the risers painted white and the treads stained. I think it looks awesome.

No one is going to mistake it for a fancy custom oak staircase, but it looks about a million times better than the icky matted carpet that was there.

I just stained ours with golden oak oil-based Minwax and then put a light second coat of puritan pine on top to make them a bit richer and the look is stunning. I sanded well first and painted them with water then waited about 10-15 minutes for it to soften the grain to accept the stain evenly and then used a foam brush and a rag to apply the stain. I also did the sides as well. The risers were given a coat as well but are made of Masonite so I may paint them white but for now they look excellent.

There are stain-grade pine stairs and carpet-grade pine stairs; the latter are the knottiest material you'll ever see. The former is nice clear stock, very stainable if the wood finisher knows how to work with yellow pine.
Casey

I had my basement pine steps sanded and finished and they were gorgeous. However, we decided to add a carpet runner down them for safety- both for young kids and older adults- it seemed a shame to cover them up but the wood does shows a little on the sides. I would have preferred the bare steps but function over form in this case. You can have the pine stained to any shade that you want.

We used pine treads and risers from Lowes on our stairs. I painted the risers white to match all the trim in the house and stained the treads with a cabot stain that I don't remember the name of. You have to use several coats of poly over the stain or so I was told. I think I used four coats, sanding lightly between each coat. They turned out nice but pine is soft. The dog's claws have left some scratches but it still does not look bad at all. I see it has been a few months since you posted. Did you finish the stairs yet? If so, how'd they turn out?

This is an old thread but if anyone is still around - Jdez, how have your steps held up? My wife and I are building and we stupidly selected stain grade pine with a starter stair. It is going to cost 4500$ to replace the treads with oak. Suggestions if we should do this? It has a starter stair so will probably get beat up badly. Otherwise we stain the pine and hope for the best.