Kim, I suggest that you sand with 150 grit paper. Use a sanding block on flat surfaces of the molding where you can. For the rest, take a sheet of sandpaper and cut it into quarters with a sharp knife from the back. Each piece will be 4-1/2 x 5-1/2". Now fold that into thirds along the 5-1/2" side. This gives you the right firmness for easy sanding as well as a lot of edges for getting into small details. You can also use a detail sander, if you have one. You just want to open up the surface and get any gunk off, not remove a lot of wood and lose the detail (sharp edges and curves) of the moldings.
When you have done that, you can use Minwax Pre-Stain Wood Conditioner or a spit coat of shellac. A spit coat is one part white shellac to five parts denatured alcohol mixed in a metal container. An old coffee can works great and you will not need more than about a third of a can at a time. Apply this with a foam brush and it will dry very quickly. If the surface feels gritty, VERY LIGHTLY (can't emphasize LIGHTLY too much) sand with 220 grit in the same way as before. Now tack rag to get up any residue.
You are now ready to stain. The pores will be open to accept the stain but the wood should not give you streaky or blotchy staining. Apply the stain, let it set 15 minutes and wipe off any excess. Repeat if necessary.
For what it's worth, if you are in most of the middle of the country, it probably is white pine. There was a lot of that logged 80-120 years ago but it is a lot less common today because it is slow growing and more dense than the pine we see today. It could be a lot of other woods if you are more toward the 3 coasts.