First determine if it is a single stage paint or clear coat. Take a white towel and put some non-aggressive polish on the towel and rub on the paint. If you get brown paint then it is single stage, if you do not get brown it is clear-coated.
My suspicion from the looks of the paint it might have been repainted? How recently? Could be a clear-coat if recently, that is in the last 10 to 15 years.
The paint seems to be in good condition and to be too aggressive on it will cause more problems than you will correct. In fact, it looked like there were few problems.
I would start with a dual action buffer, not a rotary and a foam cutting pad and a microfine compound and see if that works for you.
If that does not give you the result you are looking for then go to a rotary buffer with a foam cutting pad and the microfine compound and see if that gives you the result you want.
If that does not, same tool, same pad but move to a light (2000 grit) compound.
That should do it I am sure.
Follow that with a foam finishing pad and either the dual action buffer or the rotary at a slower speed and a swirl remover/polish.
Follow that with a hand or orbital applied wax, better yet a paint sealant.
Let me know how this comes out.
Regards
Bud abraham