Bridge and engine rooms boost all the other rooms.
For example, a weapon room with no people in the bridge will function at 50% its maximum capacity, which I assume means that the weapon recharges half as fast as it otherwise would. The bridge contributes 25%, the engine room contributes 25%. Thus one person contributes about 6.25% to each room.
This adds up to quite a lot when you have a lot of rooms. The small boost is also cheaper than getting most room upgrades. However, make sure that you have at least one staff in the small rooms first, because the rooms would not function without staff.
One tactic is to constantly keep your bridge and engine room staffed, so that the dodge and shield generator constantly regenerate the shields fast enough to prevent invaders from teleporting in.