You can have people manning the shields, weapons and engines to improve their effectiveness (and I usually man them in that order).
I switch off power to the medbay except when I'm using it.
You can vent air out of sections on fire to put out the fire, if you have a series of doors between that fire and an airlock. Don't have your people in airless rooms.
I usually upgrade my doors once in the second sector. Slows fire spread and slows invaders.