I am having the same issue with my 2006 impala. I religiously change my oil and my oil light comes on, I get the low oil pressure warning telling me to stop engine, then it goes off again. Stays on for maybe 30 seconds each time, then shuts off. Do I just need to replace the 2 parts mentioned above or will I need a new oil pump also?
Depends on what's really happening. The screen and sensor are an easy cheap fix. If the screen is clear and the sensor is working properly it's time to put an oil pump in.
I usually just replace the pickup tube and screen when I do an oil pump.
If your 06 has AFM Displacement on Demand replace the oil pan gasket with the updated GM gasket listed in the LS4 oil consumption TSB 11-06-01-007... even if you aren't using oil.
A Melling oil pump will come with more than one pickup tube O-ring. Pick the right one for your rig according to the instructions.
I use a pickup tube brace or girdle depending on what you want to call it to keep the pickup tube from tilting in the oil pump inlet...
Be sure to properly centre the gerotor in the oil pump housing. Aftermarket oil pumps and even stock GM oil pumps have pretty tight clearances to the gerotor setup so it has to be properly setup to avoid damaging the new pump. There are horror stories of cracked gerotors that could've likely been avoided if the pump housing to gear relationship had been setup properly.
This is a Melling 10295 but it applies to all of the LS engine oil pumps.
Once that's done prime the pump.