Certainly you do not want to sandpaper (rub down) any stain blocking product like Zinser since you will scratch through the product. Any sanding needs to be done before you apply any paint.
OR certainly not apply any product over the top of the wallpaper paste!?
You need to wash off the paste with sugar soap until the wall is no longer sticky AT ALL, this will take several times of washing with warm sugar soap and you can scrape off the paste as well. At this point, before you apply any paint, use caulk and filler to fill any holes and cracks. If you want nice looking walls, it is all about these preparation steps. Zinser is expensive, you can just use any oil based undercoat to seal the woodwork. Then paint as normal.
Actually it may not be necessary to use a stain block since not all wood produces stains that go through emulsion or vinyl matt paint. Also the stain block paint tends to be non permeable and is the equivalent of wrapping your walls in clingfilm with the associated risks of causing water retention or condensation which does not happen with permeable paint.
As you can see it is a complex process and without experience your chances of getting it right are pretty slim and that is why people hire professionals.