Re: Sanding between coats
Use 220 for smoothing the primer and between coats, the latter only if necessary.
Tips: paint the panels first; use a roller to get paint on the door rapidly, then immediately use a good brush to smooth it out. If your paint is drying very fast, wipe any excess overage that gets on the stiles and rails, otherwise they will not blend. Do the stiles and rails always with the grain, which means in the specific order dictated by the pattern of the door; the short stiles between panels get done first, so the brushstrokes of the next frame parts will catch their overages. The side stiles are always the last to be painted, as they catch the overages of the rails.
Another tip: remove the knobs and mask the hinges.
In hot weather you need to work like mad to keep ahead of the drying paint and get a neat job.
Or, rent an HVLP sprayer and avoid those headaches.
Remove not the ancient landmark, which your fathers have set.