I don't know what a dry sink is but that shouldn't matter. If the piece is as smooth as you want it to be then there shouldn't be any need to sand it more unless you think there might be some sort of coating on it that would prevent stain from getting into the wood. If that is the case then you could hit it with some fine paper, maybe 150 grit, lightly, with the grain.
Your best bet is to try to test whatever you are going to do, either on an area that will never be seen on the piece or on another scrap piece of the same kind of pine. Otherwise you will have no way to predict what it will look like. I usually purchase several of the small cans of Minwax brand stain and try them out on similar scraps first. sometimes I even blend them to get the color just right. Remember to stir, stir stir! All the pigment is likely to be settled down into the gunk at the bottom of the can. Usually I drain off 80% of the liquid and stir the gook completely, then add it all back together. Stir frequently while staining to prevent further settling. Follow the directions on the can, apply, wait a few minutes or not, then wipe off excess. I almost always use polyurathane after, though not required for all jobs.
For pine I almost always use minwax wood conditioner first. This is put on, wiped off and apply stain within an hour or two, whatever it says on the directions. This stuff gets absorbed by any very porous areas that are common in soft woods and helps minimize the very dark, blotchy areas you can get with staining soft wood. Keep in mind if you use this stuff that the stain won't absorb as much EVERYWHERE and that because of this you will need to use a darker stain than if you didn't use it. If you use this stuff then also use it the same way on your test pieces.