I like the headlight cleaner stuff. Fixed my TT cover. Whatever you use, if you use a polishing machine or sander it must be random orbit or swirls will come back.
With regards to the type of polisher:
You
can use any kind of polisher and get good results polishing clearcoats --- If you use good technique
And yes, random orbital is generally more forgiving & easier to learn on compared to the traditional rotary polishers.
However, Random orbital polishers have one major issue in that they are limited by the ability of the weighted polishing head to overcome the force applied by you. In other words, if you apply too much pressure, the head can stall out and the orbits become consistent, making swirl marks
really bad.
Personally, I like the idea of the geared orbital polishers. By using gearing to get the rotation and orbit motion, everything is directly driven by the motor, and as such won't stall out as easily. However, it is not a random orbit, and so more care must be taken to limit swirls...
But really, the most important thing is to use a tool that you know how to use properly. Technique trumps tool choice (as long as the tool can do it) in this scenario
Good luck