94 Lexus LS400 fuel pump makes noise for a few seconds when starting the car then goes away and doesn't come back until I shut the car off and then if makes the noise again for a few seconds more and then goes away. It sounds like a noisy fuel pump and the noise is coming from the fuel tank.

The car runs fine with no other problems. Could the fuel filter or fuel regulator cause this problem or should I just replace the pump?

Replacing all three isn't in the budget.
Which should I change first?

Fuel filter, Fuel Pump then regulator?
Could the regulator even cause this problem?
What do you feel the problem is?

Thanks