Okavango, it may be an obvious question, but what does the POH say?
I would expect the authors of that document would have taken your worries and the actual layout of the fuel system (how many tanks, length/diameter of fuel piping, collector tank or not, typical fuel usage during taxi/runup, ...) into account and written their procedures accordingly.
The PA28-161 Cadet POH (1989 edition) I have here for instance only specifies that before starting the fuel selector should be "moved to the desired tank" (without specifying what the desired tank is or should be), and before takeoff that you should "check the fuel selector to make sure it is on the proper tank (fullest)".
There is no mention anywhere of the practice of starting on the least full tank and switching to the fullest before the runup.