Hi first please be very careful sanding these door down as the old paint is very likely to have lead in it, good quality dust mask and sand outside if possible. Which Zinsser bin did you use? There are three, water, solvent and shellac based
If it was the shellac based "primer, stain block", my preferred for this kind of job because of how hard it drys to and seals the wood, I would this on the door as its less prone to to sanding damage during preperation. This is how I would go with the job.
Step one, in exellent, bright light, I also like to use an inspection lamp at an angle as well, use a good quality wood filler, I prefer "Tetrion Professional Woodfil Two Part ", its easy to work and does an exellent job, give each rough edge flake a thin covering with the filler and allow to go off, a good quality binary compound filler will not take long. During this stage seal any knots you can see with a shellac based sealer, three or four coverings at least.
Step two, it is a personal judgement of the grade of sand paper you start with, 80 grit if its very rough, or 120 grit if its not too bed. Sand each filler lump until you cant feel a lump or edge. Dust the door, then wash the door and allow to dry fully, be careful washing any exposed wood grain as it may swell and hold the water making sanding and painting awkward.
Step three, use masking tape to cover door furniture, handles and hinges, then undercoat, I would use Zinsser shellac based as a first undercoat, then when dry, inspect in exellent light again and you will see the first undercoat will highlight lumps and bumps you missed the first time you sanded.
Step four, sand anything you missed the first time that a single undercoat has highlighted, then fill once more. Sand the filler, dust and wash the door, apply another undercoat, following undercoats I would use dulux quick dry primer undercoat.
Step five, repeat step four, if your hinges are painted over, then now is the time to remove them and soak in paint stripper and remove all old paint, same with all door furniture, it really will make a difference to the finish, wire wool is a help. From now on it is fill, sand, dust, wash, dry then another undercoat. I may change from dulux quick dry to the oil based undercoat as the last coat of a day so it has the entire night to go off, but not important.
When the door passes inspection, it may take several fills and sandings before its ready for the top coat. Only when perfectly smooth and the only colour you can see on the door is the undercoat, now and only now is it ready for a single top coat of your choice.
I hope this helps.
Duncan