Decorators' caulk works best on narrow gaps that are subject to slight movement because it flexes a bit with movement. Being supplied in a tube it is also quicker to apply. Wood filler is better if you are matching the colour of the wood because you want to coat in polyurethane or similar, where the wood grains show through. You can fill bigger holes with wood filler (though more than one application may be necessary).
For what you are doing (painting the doors afterwards), I'd use whatever is easier - which may be a combination of both.
The best finish is always obtained by several thin coats and light rubbing down between. But it depends how fussy you are. You are clearly hoping to get away with only 2 coats of finish in total. Since you are saving money by re-using the doors, depending on the value you place upon yout time, perhaps best to consider 3 coats anyway. The first one being a decent primer.