It's actually all SWOS Basic Division Officer course now. No more SWO Intro. BDOC started its first classes back in October and is now the baseline training course for all new SWOs. It lasts 8 weeks and is held in Norfolk or San Diego, depending on which coast your ship is on.
As for where you can expect to go and for how long immedeately after commissioning... Unknown. You may be sent to some other school for a few weeks to get training related to your primary or a collateral duty. You may get ordered straight to the ship pending a BDOC quota. The issue is that, as with every major new accession school, it has limited throughput that sometimes can't accommodate all new officers in a given period: if you're graduating OCS in the spring, particularly after May/June, you may be "stashed" at your ship for a few months, then get sent to BDOC after a few months.
You won't know for sure until you get your PCS orders to your first ship.