In my limited (3 months) experience with the Cyclo and for a short while with Optimum polish, I found that the OP didn't do much in the way of correction of moderate swirling. With any of the pads. I've got all of the Double Precisions, except wool. To be fair, I never tried the Optimum Compounds though, so I'll not diss the Optimum polish line. I use the ONR and love it.
I've since moved on to try
Meguiars #95, #83, #80, and
Menzerna FPII, and found that they work pretty well, again in my limited experience. There's so many products/brands out there, it borders on the absurd. The Cyclo does seem very friendly, in that I think it would be very difficult to do much damage in any way, while you're learning.