So you have a symphony of sounds when your car starts.
I am currently enjoying a screeching sound when starting from cold for around 5 minutes that is due to the non genuine aux belt tensioner.
I would check that out, as soon as you have started the car, place a spanner on the notch used to de-tension the belt and move it slightly either way and check for change in noise. Be careful though, fast moving belts and pulleys tend to rip off things that get trapped in them.