Something that hasn't been mentioned ... A good coat of wax will aid in the "diminished look" of swirls and fine scratches. Not only is wax a protectant, it also does an excellent job of "filling" the scratches and diminishing the look of imperfections in the paint. Darker colors are worse for the look as they have a higher "reflective quality". As my signature says "Black, of course" ... because it is THEE fastest and best looking ....... :>)

 

I would start with the least abrasive polish to start with, and if that doesn't work, go to something with a little more abrasive. You don't want to go with an aggressive
sanding to start with. You can always go with more, but if you don't know what you are doing, and damage the clear, you will be worse off than when you started.
Start low and work your way up on the scale IMO.

 

Tried it once. Left more scratches & swirls than I originally had.