Hi, Fred. On the wainscotting and doors, I think that shellac is a good choice. The problem is the stairs. I suggest that you consider doing the treads only or the treads and risers with poly and do the rest of the wood on the staircase with shellac. I don't feel that shellac is the best choice for stairs since it is not as abrasion resistant. And, if I were doing it, I would use a good oil based poly.
If you can control the traffic on the stairs, you might consider finishing every other tread one week and the remainder the next week. If you have people that are likely to forget this in the house, you might have to go with another plan. But if you do go this way, you can mark the first treads don't with painters tape and tell them to step on the tape. And ask them not to wear metal tipped riding/cowboy boots on the stairs anytime. It's not too difficult to fill the scratches in but it is something that you would rather not do. And, yes, I speak from experience.
Good luck and let me know if I can be of any more help.