Ok my final 2 cents worth on this thread.
Too many years ago when learning to fly the very forgiving PA28-140 the fuel management was this - and a confession - I cannot tell you what the POH says because this it what the instructors drummed into me!
Always start the engine off the tank with the lesser quantity of fuel - if applicable.
After start change to the highest (or other tank) - the idea being that for take off you were using the tank with the most fuel and if there was a blockage or flow problem it would manifest itself prior to takeoff.
After that change tanks every 30 minutes - fuel pump on - change tanks - record change in flight log - fuel pump off.
Did this VFR or IFR - for IFR it was "mandatory" in so much as it was part of the regular cruise checks.
Never suffered a fuel related problem which of course was a combination of good luck (no mechanical pump failures etc) and good fuel management.
Safe flying.
Indianzz