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Indian Ports

Here you have a List of all Indian Ports :

Silk : Yanam, Calcutta, Vizagapatam
Spices : Goa, Bombay, Surat
Tea : Cochin, Madras, Masulipatam
Porcelain : Port Blair, Ache

I think Goa, Bombay and Surat are the closest ones.
And don't forget to fill up your cargo holds with Marines if you want to capture a Port.

RC
 
And Matara on Ceylon. 12 total.

Getting a Spices port first is the most beneficial in the long run since Spices provide best profits.

Also, you don't have to finish this mission at all. You can disregard it completely (advised on Hard difficulty) or fail it. Nothing bad will happen except you will have to build such a fleet yourself (easily done by 1615) and take those ports with own ships.

AI won't start taking ports right away if you fail the mission, they will wait till around 1620 with that so you won't be behind at all during those years. If you succeed in this mission though, AI will start taking ports right after you've got yours.

So this mission is basically your choice whether you want everyone to have an own port 12 years sooner than they normally would.