With the Minutemen settled in Sanctuary Hills and a couple Radiant quests under your belt, now is the time to set up a proper military base. One fitting locale is Fort Independence, a far off fort in South Boston. It's a bit of a trek, but at least you'll gain experience encountering hostiles and discovering new places.
Meet Preston Garvey at the snack shop just outside of the fort. As the team prepares for the assault, you'll get to decide how to attack — directly as a group or split for a pincer maneuver.
The meat of this quest is essentially a bug hunt. Kill the Mirelurks and destroy the eggs. Eventually, the queen will appear. Use the wide open spaces of the castle interior and exterior to your advantage. There's no shame in backpedalling. This is also a good opportunity to get targeting practice with the VATS, since the queen is more vulnerable in some areas than others.
With the hostiles all taken care of, it's time to let the world know the legitimacy of The Minutemen. Using the shack at the center of the area, build a radio transmitter at the workshop. Since it will need 10 units of power, you'll need to build two generators that power five units each. Attach wires from the generator to the transmitter to complete the quest.