First I like to use only latex on the inside unless I am doing base boards and trim.
I would first clean the stained door with a good cleaner, then rough up the stained door with sandpaper sanding in the direction of the grain. Only roughing up the surface. Then apply a good latex primer like Zinzer. Apply two light coats. Allow to properly dry between coats. Then apply your two coats of top coat. Paint of preference, Sherwin William's.