Unless they've changed something in recent years, you cannot STAR at a training command in a student status. So given that, you must wait until you get to your first sea command.
IF you are chosen for Staff pickup, you will be STAR reenlisting at NPTU. Your tour there will be 24 months, generally speaking.
As for your warfare pin, when I retired in Dec 2011, the rules (for surface sailors) were you had to receive your warfare pin within 24 months of reporting to your sea command.
Lastly, there is NO warfare pin earnable while stationed at NPTU.