It depends on what your goals are. Adding sprints to your jogs will train some more leg power and burn fat. Steadily jogging, on the other hand, will allow you to go longer and train more endurance.
If you want to burn more fat, then running in a fasted state is better. If that's not what you're focusing on, though, have some small, light snacks in the hour or so before running.
And yes. Always drink water.
