fuel & engine start
Just to clarify:
Fuel tank selection is not important for engine start. If there is fuel available in any tank, that fuel will be used.
If there is fuel in the centre tank and the centre pumps are on, due to a higher pressure operation (to allow centre tanks to be drained first), the engines will draw fuel from this tank. Otherwise, the fuel would be drawn from the wing tanks.
The need for the wing tanks to be full with more than 453 Kgs in centre tank is a structural limit (or recommendation from boeing).
Also, the centre pumps are switched off with less than 2300 kgs (varies depending on company SOPs) for start and take-off simply to avoid annoyance warnings of 'low-pressure' warnings in the centre tank due to the position of the detectors and gravity in a climb !
Hope that helps !