Speaking as a DIYer (not a professional) I'd rub down with high value grit sandpaper (180 or above depending on the surface) just enough to take the shine off the surface and give the paint something to key to.
Most undercoats nowadays are combined "primer/undercoat" (and mostly non-solvent based too). I'd give it two coats of a combined primer/undercoat and then one top coat. Rubbing down gently between coats should give a better finish.
The doors in your picture look like panel doors; not too sure how well they will rub down.
Another tip is to take the doors off their hinges and paint them laying flat. This will help avoid streaking of the paint...
Finally, these layers of paint will add height to the doors/frames so you might need to take a bit off the top and side of the doors before you paint them to make sure they fit after...
Best of luck!
I would pretty much agree with the advice above. Just to add don't go too heavy on the rubbing down otherwise any scratches will show through any paint finish. Also give the doors a wipe over with white spirit or similar just to make sure there isn't any residue (someone might have used polish on them in the past).
I would definitely think about 2 or maybe even 3 undercoats to completely obliterate the dark wood before top coating, with a very light sand/de-nib in between coats. Flat panel doors will show all the imperfections unless your prep is meticulous.
Its a good idea in practice to degrease with something like white spirit or meths but water based primer aint gonna like that.
An ordinary wood primer won't be a strong enough bond and will chip very easily, you need to use a high grip primer like zinnser 123, dulux super grip and blackfriars do one which i can't remember the name of. Instead of rubbing it down and risking scratching it you could use the liquid prep stuff which name escapes me as well, its called something like MSP i think.
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