I love the look of a white bead board or pine ceiling however what your going to have the biggest issue with is the knots bleeding through, As it gets older the more you will se the tannin acids also bleed. Now this is not necessarily a bad thing as it takes on a distressed kind of French appearance but there are a lot of knots. Depending on the flooring is what would decide the the ceiling. If you want a solid white ceiling you are going to have to use a shellac sealer first to seal that wood or you could spray it with the Oil base Kilz or even a Slow cure Oil like Sherwin Williams A-100 primer and let it cure out for at least 24 hrs between coats. From the way the pitch is I would spray two thin coats of the primer to keep it from "sagging". I know it sounds like extra work but this will stop any bleed through and prevent those knots from showing just make sure yo have filled and sanded any cracks associated with the knots.
Personally I love a pickled white wash stain look and you can make this from an oil base stain or paint and not have to worry about the bleeding as it just adds to the weathered look. However use a warm white as the cooler whites which are blue will make it appear green but this would look good with a natural American Walnut flooring if you so choose.

A quick tip on staining or pickling the boards is to do them individually (one at a time) for uniformity and not in sections to prevent "laplines" In this instance I would advise using one of two products Zar makes a beautiful pickling white. However for the best and more user friendly I would use Sikkens as you can just brush it on and theres no wiping. You could just brush on two coats of the Sikkens and be done and it looks stunning, get a few scrap pieces of the pine and do some large samples first however before deciding anything. You could even give a little distressing after it dries simply by hitting a few edges with some 220 sand paper here and there just don't over do it.
Peace!