Nobody can comment on the accident at the beginning of this thread as nothing is known but talking about fuel management before take off.
There seem to be 2 schools of thought.
One is that you start and taxi out on the lowest tank and then change to the fullest before you do the run-up and engine checks leaving it on that tank for the take-off and initial climb.
That works indeed well for most aeroplanes with shortish fuel lines.
The other method is to start on the fullest tank and taxy, run up take off and climb on that tank until you are in the cruise and then change. Advantage is that you know that your fuel supply is good and uninterrupted. Drawback is that you don't know if the other tank(s) are feeding.
Best thing to do is to use your POH or noddle and work out something that works for you and your aeroplane and stick to that.
FD