We want to paint our living room but there is a fine but noticeable film of soot on the walls and ceiling. This was from a free-standing propane stove that was smoking due to improper log placement, but now has been corrected and no longer smokes.

Do we need to clean the soot off the walls and ceiling before we paint, or can we just put on a coat or 2 of a primer such as Kilz? Can we use Kilz on the ceiling, before a ceiling paint, or is it only for walls?

Does anyone have any experience with using a paint and primer all in one, such as Behr?

Clean the walls and ceiling first using TSP. You can use Kilz-It on the ceiling. Just be sure to get a water based primer.
I have never used the primer and paint in one. Primer is much cheaper than paint so see what the cost difference is between buying primer and paint or the paint with primer in it.