The best way to play Pirate Ship is to ignore it completely. If you abide by this simple and elegant heuristic you'd be making a mistake on approximately 0.1% of randomly generated boards, and this is certainly not one of them.
DG is far too modest in suggesting "maybe even mercenary"; anything but an Urchin/Urchin/Urchin open should be losing here, and losing hard at that. I'm not 100% sure whether you want a Silver or NV on T4, I'd definitely go for the NV myself but the Silver is safer if you don't feel entirely confident. Get the Mercenary as soon as you can, then trash down aggressively, get a few Treasuries and two Graverobbers.
The plan is to Graverob a Treasury into a Province and then grab it back right away.
If your opponents aren't playing discard attacks somewhat frequently (as they weren't at all in this game), I'd get a 2nd NV, otherwise I'd keep it at one. With 2 NVs your deck is going to look like this at some point: 2+ Treasuries, 2 NVs, 2 Graverobbers, Merc. If you can get the Merc on the mat you're guaranteed to get 1 Province/turn from that point onwards: draw until you have your NVs and Graverobbers in hand, don't play your last Treasury. Then play NV, putting a card from your now empty deck on the mat, play Graverobber to trash Treasury into Province, play the other NV to place the gained Province on the mat, then play the other Graverobber to get your Treasury back. If you can't get the Merc on the mat anytime soon it will be a bit more chaotic, but you should still be winning easily. On what you expect to be your last turn you should double Province, as there's little point to getting your Treasuries back.
Edit: if you can't get your last Merc on the mat after it has become useless, I'd just graverob it into an Urchin, draw the Urchin and Graverob that one into another Treasury. It'd just be so nice if you can guarantee gaining a Province and putting it on your mat each turn that it's well worth waiting an extra turn to start greening.