Here's my perspective, from one newbie to another...
A couple months ago, I was in exactly the same situation as you: swirled paint, and the desire to correct it to perfection. Luckily, the wife got me a PC for Xmas (poor thing had no idea what she was starting...) Anyway, to make a long story short, here's what I think you should do, as this process is easy, and really safe...
4" pads are the ONLY way to go for hard clear coat paint correction on the PC. Anything larger, and you just can't get aggressive enough.
Start out with Menzerna Power Gloss on a 4" Yellow LC CCS pad. This product is really pretty safe on both Ceramiclear and traditional clears. Since you don't know which one you have, it's a pretty safe starting place.
Check the level of correction you achieve, and the amount of polishing haze. If you haven't gotten good correction results, chances are you have a scratch resistant clear coat. (Which is what happened to me... Power Gloss didn't do much correction at all).
Next step, assuming you have a scratch resistant clear, use a new 4" yellow pad, and try out a few passes with Blackfire Scratch Resistant Clear Compound. You should achieve some pretty good correction with this stuff. Don't be surprised if it takes three or more applications to achieve the results you're looking for; it's really hard to correct scratch resistant clears with a PC.
After you've achieved the correction you're looking for, use a green LC pad (I haven't been able to find them in four inch size), and use Menzerna PO106ff. Alot of guys would argue that you should use a white pad for this, but in my limited experience, a PC with a green pad is about equal to a rotary with a white pad in aggressiveness on scratch resistant clears, and gave me much better results than a white pad. This step should get you to the finish you're looking for.
Now go over the entire car with a isopropyl alcohol wipe down.
Now you're ready for your LSP.
I used ZAIO applied with a white LC pad, followed by three coats of ZFX'd Z2 applied by hand.
For what it's worth, this really is a safe, newbie-friendly process that should produce the results you're looking for.
Edit: Why the ZAIO prior to the Z2? It wasn't to remove the traces of the polishes; that's what the alcohol wipe down is for. I had heard that ZAIO adds a bit of "warmth" to a Z2 finish, so it doesn't look so artificial and plastic-y. That's one of the things I don't like about Zaino... it looks very artificial (for lack of a better term). I've been very happy with the finish. The ZAIO really does make the shine look more warm and carnauba-like. The only thing I now dislike about Zaino is it's affinity to holding onto dirt and dust, but that's a topic of another post... :hmph: