Don't know much about the finishing coats etc, but firstly the seal (varnish) needs to be broken i.e. sanded and then a fine coat of aluminium wood primer needs to be applied as teak is a hardwood to allow the paint to stick properly.
Where I work everything is manufactured in teak and some architects (where it is going to be paint finished) specify an aluminium wood primer finish. It can be got in a grey or white finish.
Then follow this with undercoat and whatever gloss/matt etc finish coat that you fancy!
I have recently painted a teak door and agree with what NHG suggested. Firstly, I sanded the door (the hardest part of the job!!), then wiped with White Spirits, then applied the aluminium wood primer followed by a coat of undercoat and then the gloss (green).
I painted the inside of the door white, so internally I used a white primer, not sure if this was correct, but it seemed to work ok.